grade 9 math algebra question!

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 j = John's age

Let a = Amber's age

 

John is 3 years older than his sister Amber:

j = a + 3

 

product of their ages is the same as their father’s age... father is 40 years of age:

ja = 40

 

Using substitution replace j with a+3 in 2nd equation

 

a(a+3) = 40

a² + 3a = 40

a² + 3a - 40 = 0

 

This can be factored.  The factors of -40 that add to 3 are 8(-5):

 

(a+8)(a-5) = 0

Either:   a+8 = 0 and a= -8

OR:   a-5 = 0  and  a = 5

 

Disregarding the negative, Amber is 5 years old

 

Since j = a + 3 = 5 + 3 = 8

        John is 8 years old