A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>At a game show, Ming was given&nbsp;$20$ multiple-choice questions. He gets $5$ points if he answers a question correctly, gets a point if he does not answer a question and gets $2$ points deducted if he answers a question wrongly. If Ming answered at least a question wrongly and scored $52$ points at the game show, find the number of questions he answered wrongly.<span class="inline-marks">[4]</span></p>

At a game show, Ming was given $20$ multiple-choice questions. He gets $5$ points if he answers a question correctly, gets a point if he does not answer a question and gets $2$ points deducted if he answers a question wrongly. If Ming answered at least a question wrongly and scored $52$ points at the game show, find the number of questions he answered wrongly.

Linear Inequality

Systems of Linear Equations in up to Three Variables

Integer and Feasibility Constraints in Linear Models

Application of Simultaneous Equations in Real World Contexts

2026 HCI P1 Q1

Inequalities

System of Linear Equations

<p>Phoebe has $20$ orange-flavour candies, which is $80\%$ of the total number of candies she has, and the rest are peach-flavour candies. Rachel has in total $50$ candies, of which $30\%$ are orange-flavour candies and the rest are peach-flavour candies. Rachel gives some of her candies to Phoebe such that Rachel has now $40\%$ of orange-flavour candies and Phoebe has now $50\%$ of orange-flavour candies. Find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the number of peach-flavour candies Phoebe originally has,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of orange-flavour and peach-flavour candies Rachel originally has,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of candies that Rachel gives to Phoebe.</span></div></li></ol>

Phoebe has $20$ orange-flavour candies, which is $80\%$ of the total number of candies she has, and the rest are peach-flavour candies. Rachel has in total $50$ candies, of which $30\%$ are orange-flavour candies and the rest are peach-flavour candies. Rachel gives some of her candies to Phoebe such that Rachel has now $40\%$ of orange-flavour candies and Phoebe has now $50\%$ of orange-flavour candies. Find

the number of peach-flavour candies Phoebe originally has,

the number of orange-flavour and peach-flavour candies Rachel originally has,

the number of candies that Rachel gives to Phoebe.

Expressing One Quantity as a Percentage of Another

Percentage of a Quantity

 Basics of Percentage

Percentages

Simultaneous Equations

<p>There is a fraction.  By letting the numerator be $x$ and the denominator be $y$, answer the following questions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">If&nbsp;$4$ is added to the numerator and $5$ is added to the denominator, the new fraction is equivalent to $\frac{3}{4}$.  Form an equation based on the information given and show that the equation reduces to $4x-3y=-1$.<br></div></li><li><div class="list-item-paragraph">If&nbsp;$1$ is subtracted from the numerator and the denominator is multiplied by $4$ the new fraction is equivalent to $\frac{1}{12}$.  Form an equation based on the information given and show that the equation reduces to $3x-y=3$.<br></div></li><li><div class="list-item-paragraph">Hence, solve the simultaneous linear equations and write down the original fraction.</div></li></ol>

There is a fraction.  By letting the numerator be $x$ and the denominator be $y$, answer the following questions.

Simultaneous Equations: Fraction Problem

<p>The sum of the digits of a two-digit number is $9$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Letting the tens digit and the ones digit of the number be $x$ and $y$ respectively, form an equation to represent the above information.<br></div></li></ol>
<p>When the digits of the number are reversed and the resulting number is subtracted from the original number, the result obtained is $45$.</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Form an equation to represent the above information, and show that the equation simplifies to $x-y=5$.<br></div></li><li><div class="list-item-paragraph">Hence, find the original number by solving the pair of simultaneous equations from <strong>(a)</strong> and <strong>(b)</strong>.<br></div></li></ol>

The sum of the digits of a two-digit number is $9$.

When the digits of the number are reversed and the resulting number is subtracted from the original number, the result obtained is $45$.

Simultaneous Equations: Two-Digit Number Problem

<p>The radius of a small circle is $(p-2q)$cm and the radius of a big circle is $(5p-12q)$cm.</p>
<p>The radius of the big circle is twice the radius of the small circle.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down and simplify a linear equation connecting $p$ and $q$.</div></li><li><div class="list-item-paragraph">If the sum of the circumference of the two circle is $16\pi $ cm.  Write down and simplify 	another linear equation connecting $p$ and $q$.</div></li><li><ol class="i-list"><li><div class="list-item-paragraph">Find the values of $p$ and $q$.</div></li><li><div class="list-item-paragraph">Hence, find the radius of the small circle.</div></li></ol></li></ol>

The radius of a small circle is $(p-2q)$cm and the radius of a big circle is $(5p-12q)$cm.

The radius of the big circle is twice the radius of the small circle.

Circumference and Area of Circles

Simultaneous Equations in Circle Geometry

Perimeter and Area of Plane Figures

<p>Jolene can make $x$ ornaments in $4$ hours and Fiona can make $y$ ornaments in $3$ hours. Every hour, Fiona makes $3$ more ornaments than Jolene.  Together, both of them can make $(2y-x+5)$ ornaments in $5$ hours.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Form a pair of simultaneous equations to represent the above information and show that the equations can be simplified to</div><div class="list-item-paragraph" style="text-align: center">$\begin{align}
  & 4y-3x=36 \\ 
 & 27x-4y=60  
\end{align}$<br></div></li><li><div class="list-item-paragraph">Solve the simultaneous equations in <strong>(a)</strong> and hence, find the number of ornaments made by both Jolene and Fiona in $5$ hours.<br></div></li></ol>

Jolene can make $x$ ornaments in $4$ hours and Fiona can make $y$ ornaments in $3$ hours. Every hour, Fiona makes $3$ more ornaments than Jolene.  Together, both of them can make $(2y-x+5)$ ornaments in $5$ hours.

Work Rate and Productivity Using Simultaneous Equations

<p>Ann drove for&nbsp;$4$ hours at an average speed of $x$ km/h and then for&nbsp;$6$ hours at an average speed of $y$ km/h.  She drove a total distance of $816$ km.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down an equation in terms of $x$ and $y$, and show that it simplifies to $2x+3y=408$.</div></li><li><div class="list-item-paragraph">Ken drove for&nbsp;$3$ hours at an average speed of $x$ km/h and then for&nbsp;$5$ hours at an average speed of $y$ km/h.  He drove a total distance of $654$ km.  Write down an equation in terms of $x$ and $y$, to represent this information.<br></div></li><li><div class="list-item-paragraph">Solve the two equations to find the value of $x$ and of $y$.</div></li></ol>

Ann drove for $4$ hours at an average speed of $x$ km/h and then for $6$ hours at an average speed of $y$ km/h.  She drove a total distance of $816$ km.

Simultaneous Equations from Distance–Speed–Time Problems

<p>There are two numbers.  When the second number is subtracted from twice the first number, the result is $18$.  When&nbsp;$9$ is added to the first number, the result is equal to twice the second number.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Using $x$ as the first number and $y$ as the second number, write down a pair of 	simultaneous equations.</div></li><li><div class="list-item-paragraph">Hence find the numbers $x$ and $y$.</div></li></ol>

There are two numbers.  When the second number is subtracted from twice the first number, the result is $18$.  When $9$ is added to the first number, the result is equal to twice the second number.

Simultaneous Equations: Number Problem

<p>A farmer rears $x$ ducks and $y$ horses.  If the total number of ducks and horses in the farm is $71$ and the total number of legs is $180$,</p>
<ol class="abc-list"><li><div class="list-item-paragraph">form two simultaneous equations in $x$ and $y$.</div></li><li><div class="list-item-paragraph">Solve the equations to find the number of ducks and horses the farmer rears respectively.</div></li></ol>

A farmer rears $x$ ducks and $y$ horses.  If the total number of ducks and horses in the farm is $71$ and the total number of legs is $180$,

Simultaneous Equations: Ducks and Horses Problem

<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764492540883-s4d37hwj3ub.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0OTI1NDA4ODMtczRkMzdod2ozdWIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUxMDkwMywiZXhwIjoxNzkzNTExMjAzfQ.Td8LhgTYp3NB8e94dghpFUkv3i0M3s9_kEo_fTIhklo" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>In the diagram, $ABCD$ is a rectangle.  Given that&nbsp;$AB=\left( 2x+y \right)$cm, $BC=\left( x+y \right)$cm, $CD=\left( 3x+5y+3 \right)$cm and $AD=\left( 4x+5y-7 \right)$cm.<br></p>
<ol class="abc-list"><li><div class="list-item-paragraph">Form two equations involving $x$ and $y$.</div></li><li><div class="list-item-paragraph">Find the values of $x$ and $y$.</div></li><li><div class="list-item-paragraph">Calculate the area of rectangle $ABCD$.</div></li></ol>

In the diagram, $ABCD$ is a rectangle.  Given that $AB=\left( 2x+y \right)$cm, $BC=\left( x+y \right)$cm, $CD=\left( 3x+5y+3 \right)$cm and $AD=\left( 4x+5y-7 \right)$cm.


Perimeter and Area of Rectangles and Squares

Solving for Dimensions of a Rectangle Using Simultaneous Equations

<p>At a Korean buffet restaurant, adults are charged at a fixed price and children are charged at a lower fixed price.  The total cost for&nbsp;$3$ adults and $4$ children is $\$108$, while the total for&nbsp;$5$ adults and $2$ children is $\$124$. <br>Let&nbsp;$\$x$ be the cost for an adult and $\$y$ be the cost for a child.</p>
<ol class="abc-list"><li data-list-item-id="item-1764489637580-2pu5daslh" data-list-item-path="item-1764489637580-2pu5daslh"><div class="list-item-paragraph">Form two equations involving $x$ and $y$.</div></li><li data-list-item-id="item-1764489638578-egzzxwl83" data-list-item-path="item-1764489638578-egzzxwl83"><div class="list-item-paragraph">Hence, find the cost for an adult and a child.</div></li><li data-list-item-id="item-1764489639808-totc1p6km" data-list-item-path="item-1764489639808-totc1p6km"><div class="list-item-paragraph">Find the total cost of $6$ adults and $2$ children.</div></li></ol>

At a Korean buffet restaurant, adults are charged at a fixed price and children are charged at a lower fixed price.  The total cost for $3$ adults and $4$ children is $\$108$, while the total for $5$ adults and $2$ children is $\$124$. 
Let $\$x$ be the cost for an adult and $\$y$ be the cost for a child.

Finding Costs Using Simultaneous Equations

<p>The cost of a cup of coffee and a cup of tea is $\$x$ and $\$y$ respectively.  A customer bought two cups of coffee and three cups of tea at a total cost of $\$3.80$.  Another customer bought four cups of coffee and five cups of tea at a total cost of $\$6.90$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down $2$ equations in terms of $x$ and $y$.</div></li><li><div class="list-item-paragraph">Hence, find the cost of a cup of coffee and a cup of tea.</div></li></ol>

The cost of a cup of coffee and a cup of tea is $\$x$ and $\$y$ respectively.  A customer bought two cups of coffee and three cups of tea at a total cost of $\$3.80$.  Another customer bought four cups of coffee and five cups of tea at a total cost of $\$6.90$.

<p>At a breakfast restaurant, the first group of customers buy $4$ toasts, $3$ bagels and $3$ glasses of milk, which cost $\$35$ in total; the second group of customers buy $4$ toasts, $2$ bagels and $5$ glasses of milk, which cost $\$36$ in total; the third group of customers buy $8$ toasts, $8$ bagels and $10$ glasses of milk, which cost $\$84$ in total.</p>
<p>Find the unit price of toast, bagel and one glass of milk.</p>

At a breakfast restaurant, the first group of customers buy $4$ toasts, $3$ bagels and $3$ glasses of milk, which cost $\$35$ in total; the second group of customers buy $4$ toasts, $2$ bagels and $5$ glasses of milk, which cost $\$36$ in total; the third group of customers buy $8$ toasts, $8$ bagels and $10$ glasses of milk, which cost $\$84$ in total.

Find the unit price of toast, bagel and one glass of milk.

IP1U10 HOT Q1

<p>A dietitian wishes to plan a meal using three types of ingredients. The meal is to include $8800$ microgram $\left( \mu \mathrm{g} \right)$ of Vitamin $A$, $3380\mu \mathrm{g}$ of Vitamin $C$ and $1020\mu \mathrm{g}$ of calcium. The amount of the vitamins and calcium in each unit of the ingredients is summarised in the following table:</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760354990008-me6cbrb8yer.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjAzNTQ5OTAwMDgtbWU2Y2JyYjh5ZXIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUxMDkwMywiZXhwIjoxNzkzNTExMjAzfQ.Ktfo7N9XoIKIMFNd4_5v_vZvIOOI5wRevEg0_lttYvo" width="400" class="aligncenter" /></figure>
<p>Ingredients I, II, III cost $\$3$, $\$2$, $\$4$ respectively. Assuming that all the $3$ ingredients were used and the number of units used are whole numbers, find the combination of each ingredient in the meal that meets the vitamins and calcium requirements and that cost the least.</p><p style="text-align: right;">[5]</p>

A dietitian wishes to plan a meal using three types of ingredients. The meal is to include $8800$ microgram $\left( \mu \mathrm{g} \right)$ of Vitamin $A$, $3380\mu \mathrm{g}$ of Vitamin $C$ and $1020\mu \mathrm{g}$ of calcium. The amount of the vitamins and calcium in each unit of the ingredients is summarised in the following table:

Ingredients I, II, III cost $\$3$, $\$2$, $\$4$ respectively. Assuming that all the $3$ ingredients were used and the number of units used are whole numbers, find the combination of each ingredient in the meal that meets the vitamins and calcium requirements and that cost the least.

Dependent Linear Systems and Parametric Solutions

2018 AJC Promo Q1 [Modified]

<p>A product is sold on three e-commerce websites: Abay, BaoBao and CooL9. The delivery charges of Abay and CooL9 are $\$5$ and $\$3$, respectively. The Abay product price plus delivery is 20% more than the BaoBao product price. During a festive season, the CooL9 product price after a 5% discount plus delivery equals the BaoBao product price. The three product prices are positive whole-dollar amounts below $\$70$. Find the product price on each website.</p>

A product is sold on three e-commerce websites: Abay, BaoBao and CooL9. The delivery charges of Abay and CooL9 are $\$5$ and $\$3$, respectively. The Abay product price plus delivery is 20% more than the BaoBao product price. During a festive season, the CooL9 product price after a 5% discount plus delivery equals the BaoBao product price. The three product prices are positive whole-dollar amounts below $\$70$. Find the product price on each website.

Percentages involving Finances: Discount

2017 HCI MYE P2 Q1

<p>A certain supermarket sells only three brands of health drinks namely Mud, Soil and Rock which are priced at $\$2.00$, $\$1.80$ and $\$1.50$ per bottle respectively. <br></br></p>
<p>Discounts offered for each brand as follows:</p>
<p>$20\%$ discount when more than $80$ bottles of Mud are bought;</p>
<p>$15\%$ discount when more than $50$ bottles of Soil are bought;</p>
<p>$10\%$ discount when more than $30$ bottles of Rock are bought.<br></br></p>
<p>Andy orders $200$ bottles of health drinks from the supermarket for a company function. As the preference for each brand differs among the colleagues in the company, he has to order at least $60$ bottles of each of the $3$ brands.<br></br></p>
<p>Andy spent $\$323.05$ after an overall discount of $\$27.45$.</p>
<p>Find the number of bottles of each brand Andy bought from the supermarket, explaining your answer clearly.</p>

A certain supermarket sells only three brands of health drinks namely Mud, Soil and Rock which are priced at $\$2.00$, $\$1.80$ and $\$1.50$ per bottle respectively. <br></br>

Discounts offered for each brand as follows:

$20\%$ discount when more than $80$ bottles of Mud are bought;

$15\%$ discount when more than $50$ bottles of Soil are bought;

$10\%$ discount when more than $30$ bottles of Rock are bought.<br></br>

Andy orders $200$ bottles of health drinks from the supermarket for a company function. As the preference for each brand differs among the colleagues in the company, he has to order at least $60$ bottles of each of the $3$ brands.<br></br>

Andy spent $\$323.05$ after an overall discount of $\$27.45$.

Find the number of bottles of each brand Andy bought from the supermarket, explaining your answer clearly.

Applications of Linear Equations in Real Life

2008 TJC P1 Q5

Linear Equations and Inequalities

<p>Mr Lee has $1650$ gemstone beads and $1950$ crystal beads. He wants to use all the beads to make necklaces of three different designs: Classic, Elegant and Deluxe. The number of gemstone and crystal beads required to make one necklace of each design are as shown.</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760354086836-9bmude6ro9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjAzNTQwODY4MzYtOWJtdWRlNnJvOS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTEwOTAzLCJleHAiOjE3OTM1MTEyMDN9.1SrxN35NOkFJtK8M1z_5Vs00u3YnU-ybcaO8-C0XQbM" width="400" class="aligncenter" /></figure>
<ol class="i-list"><li><div class="list-item-paragraph">If Mr Lee must make at least one necklace of each design, find the maximum and minimum number of Deluxe necklaces that he can make.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">If the total number of Classic and Elegant necklaces that Mr Lee makes is the same as the number of Deluxe necklaces, determine the number of necklaces of each design that he makes.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Mr Lee decides not to make any Deluxe necklaces and makes only Classic and Elegant necklaces. State, with a reason, whether he is able to do so if all the beads must be used.</div><p style="text-align: right;">[1]</p></li></ol>

Mr Lee has $1650$ gemstone beads and $1950$ crystal beads. He wants to use all the beads to make necklaces of three different designs: Classic, Elegant and Deluxe. The number of gemstone and crystal beads required to make one necklace of each design are as shown.

2019 HCI C1BT1 Q3

<p>The usual selling price of a bottle of Vitamin C, Grape Seed Extract and Super Antioxidant is $\$365$ in total. During the year-end sale, two companies, Union and Vatson, offered the following discounts to their customers:</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760351248402-ta3aifyvl4.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjAzNTEyNDg0MDItdGEzYWlmeXZsNC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTEwOTAzLCJleHAiOjE3OTM1MTEyMDN9.6vfLG0rWBOA-b9ubB-zp4RHxPh3GqKcq0jtm4ko0CY8" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li data-list-item-id="item-1760351245744-b3v2pat9u" data-list-item-path="item-1760351245744-b3v2pat9u"><div class="list-item-paragraph">Find the usual selling price of each bottle of Vitamin C, Grape Seed Extract and Super Antioxidant.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-1760351246494-7xdggxr6b" data-list-item-path="item-1760351246494-7xdggxr6b"><div class="list-item-paragraph">The employees from Union are offered a further $5\%$ discount on the usual selling price of each bottle of Vitamin C and Grape Seed Extract. Determine if this additional discount will make it more attractive for the employees to purchase all the $3$ items from their own company rather than from Vatson.<span class="inline-marks">[2]</span></div></li></ol>

The usual selling price of a bottle of Vitamin C, Grape Seed Extract and Super Antioxidant is $\$365$ in total. During the year-end sale, two companies, Union and Vatson, offered the following discounts to their customers:

2020 JPJC P1 Q4

<p>Sherry has an initial sum of ${\$35 000}$ which she divided into three portions $A$, $B$ and $C$.</p>
<p>She is considering placing the portions of money into three separate banks that provide returns through savings account and investment account. The following table shows the returns on savings account and investment account provided by the three banks for a period of one year:</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1759139692443-c82zf3f2oaj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NTkxMzk2OTI0NDMtYzgyemYzZjJvYWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUxMDkwMywiZXhwIjoxNzkzNTExMjAzfQ.J4DBO_qNpa8QZhVn276dZBHyFXBCbwlMUKA-o_3_Qa0" width="400" class="aligncenter" /></figure>
<p>Sherry did some calculations and realized that:</p>
<p style="margin-left: 3rem">I. If she were to place the portions of money $A$, $B$ and $C$ into the savings accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$151.15$ at the end of a year.</p>
<p style="margin-left: 3rem">II. If she were to invest the portions of money $A$, $B$ and $C$ through the investment accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$426$ at the end of a year.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the exact amounts of the three portions of money $A$, $B$ and $C$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Sherry decides that she will place one of the portions of her money into the savings account of one bank and the remaining two portions into the investment accounts of the remaining two banks separately. Determine the maximum amount of money she can have after a period of one year.</span></div><p style="text-align: right;">[2]</p></li></ol>

Sherry has an initial sum of ${\$35 000}$ which she divided into three portions $A$, $B$ and $C$.

She is considering placing the portions of money into three separate banks that provide returns through savings account and investment account. The following table shows the returns on savings account and investment account provided by the three banks for a period of one year:

Sherry did some calculations and realized that:

I. If she were to place the portions of money $A$, $B$ and $C$ into the savings accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$151.15$ at the end of a year.

II. If she were to invest the portions of money $A$, $B$ and $C$ through the investment accounts of POSD, OCBB and Non-Standard banks respectively, her total returns will be $\$426$ at the end of a year.

Find the exact amounts of the three portions of money $A$, $B$ and $C$.

Sherry decides that she will place one of the portions of her money into the savings account of one bank and the remaining two portions into the investment accounts of the remaining two banks separately. Determine the maximum amount of money she can have after a period of one year.

Simple Interest

ASRJC Tutorial 3 System of Linear Equations Q7

<p>Suppose that in a fixed population of breakfast-food consumers, there are just three brands, $X$, $Y$, and $Z$ that share that market.</p>
<p>Suppose that each year,</p>
<p>${10\%}$ of the brand $X$ buyers shift to brand $Y$ and ${20\%}$ to brand $Z$ and</p>
<p>${20\%}$ of the brand $Y$ buyers shift to brand $X$ and ${20\%}$ to brand $Z$</p>
<p>${10\%}$ of the brand $Z$ buyers shift to brand $X$ and none to brand $Y$</p>
<p>Suppose that it is found that despite all this shifting, the market shares of these three brands are nevertheless unchanged from year to year. What are these market shares?</p><p style="text-align: right;">[4]</p>

Suppose that in a fixed population of breakfast-food consumers, there are just three brands, $X$, $Y$, and $Z$ that share that market.

${10\%}$ of the brand $X$ buyers shift to brand $Y$ and ${20\%}$ to brand $Z$ and

${20\%}$ of the brand $Y$ buyers shift to brand $X$ and ${20\%}$ to brand $Z$

${10\%}$ of the brand $Z$ buyers shift to brand $X$ and none to brand $Y$

Suppose that it is found that despite all this shifting, the market shares of these three brands are nevertheless unchanged from year to year. What are these market shares?

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