Question

Can anyone help me with a grade 9 Math Question?

John is 3 years older than his sister Amber. The product of their ages is the same as their father’s age.

If John’s father is 40 years of age, how old is Amber?

Answer 1

Let's use the simplest method - Systems of equations (Algebra) :D

Explanation:

If this is your first time encountering Algebra, do refer to the following website: https://www.wikihow.com/Learn-Algebra (because I love wikiHow).

Here, I'm assuming you know about basic operations in Algebra.

First, let John's age be `x`.
That means that Amber's age would be `x-3`, right?

The product of their ages would mean that `x` is multiplied by `x-3` or whatever order you prefer.

Anyways, the following
`(x)*(x-3)=x^2-3x`
is the product of their ages.

Thus,
`(x)*(x-3)=x^2-3x`
is equals to `40`.

Therefore,
`x^2-3x=40`
`x^2-3x-40=0`

If you've learnt the quadratic formula which is:

Or by splitting the middle term,
`x^2-3x-40=0`
`x^2 +5x-8x -40=0`
`x(x+5)-8(x +5)=0`
`(x+5)(x-8) = 0`

You would know that `x=8 or -5`.

As age cannot be negative, `x!=-5` and therefore `x=8`.
Amber's age is `x-3`, hence she is `8-3=` 5 years old.