A fruit stall sells three types of fruit packs. Each fruit pack contains apples and oranges.
Pack 1 contains 12 apples and 8 oranges. Pack 2 contains 9 apples and 6 oranges. Pack 3 contains 5 apples and 4 oranges.
This information can be represented by \(\mathbf N=\begin{pmatrix}12&8\\ 9&6\\ 5&4\end{pmatrix}\). The price of an apple is \$x. The price of an orange is \$y.
Represent the fruit prices in a 2 × 1 column matrix P in terms of x and y.[1]
Find the matrix M = NP, leaving your answers in terms of x and y.[1]
State what the elements of M represent.[1]
Pack 1 is \$6.37 more than Pack 2. Pack 3 is sold at \$11.50.
Using the answer in (a)(ii), form two equations in x and y to represent this information. Find the value of x and of y.[4]
In the second week of the month, 6705 packs of fruits were sold. The sales decreased by 36% compared with the first week of the month.
Calculate the number of packs of fruits sold in the first week of the month.[2]
On a particular day, fruits were sold in the following ratios:
morning sales : afternoon sales = \(2\frac13:5\)
morning sales : night sales = \(6\frac14:13\)
Find the ratio night sales : afternoon sales : morning sales that day. Give your answer in its simplest form.[2]
Solution:
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