Question

Larry is 2 years younger than Mary. The difference between the squares of their ages is 28. How old is each?

Answer 1

Mary is `8`; Larry is `6`

Explanation:

Let
`color(white)("XXX")L` represent Larry's age, and
`color(white)("XXX")M` represent Mary's age.

We are told:
[equation 1]`color(white)("XXX")L=M-2`
and
[equation 2]`color(white)("XXX")M^2-L^2=28`

Substituting `M-2` from equation [1] for `L` in equation [2]
`color(white)("XXX")M^2-(M-2)^2=28`

`color(white)("XXX")M^2 - (M^2-4M+4)=28`

`color(white)("XXX")4M-4=28`

`color(white)("XXX")4M=32`

`color(white)("XXX")M=8`

Substituting `8` for `M` in equation [1]
`color(white)("XXX")L=8-2 = 6`

Answer 2

`6 and 8`

Explanation:

Let the age of `Larry=x`

Age of `Mary=x+2` (Difference of their ages are 2)

Given that the difference between the squares of their ages is 28

So,`(2+x)^2-x^2=28`

Use the formula `(a+b)^2=a^2+2ab+b^2`

`rarr(4+4x+x^2)-x^2=28`

`rarr4+4x+x^2-x^2=28`

`rarr4+4x=28`

`rarr4x=28-4`

`4x=24`

`x=24/4=6`

We know now that the Age of

`Larry=6`

So, Age of `Mary=(x+2)=6+2=8`