Optional extension At the start of a particular year, Alex was $x$ years old. Bea was 5 years olde

Question

Optional extension

At the start of a particular year, Alex was $x$ years old. Bea was 5 years older than Alex, and Chen was twice Alex’s age. Two years later, the product of Alex’s and Chen’s ages was equal to the square of Bea’s age at the start of the year.

Write down expressions, in terms of $x$, for Alex’s and Chen’s ages two years later.[2]
Form an equation in $x$ and show that it simplifies to $x^2-4x-21=0$.[2]
Solve the equation by factorisation. Hence, find Chen’s age two years after the start of the year.[3]

Accepted Answer

(a) Alex: $(x+2)$ years, Chen: $(2x+2)$ years. (b) $(x+2)(2x+2)=(x+5)^2$, giving $x^2-4x-21=0$. (c) $x=7$ (reject $-3$); Chen is 16 years old.

Multi-person age equation

Multi-person age equation

Solution:

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