Question

Alvin is 12 years older than Elga. The sum of their ages is 96. What is Elga's age?

Answer 1

Elga's age is 42

Explanation:

Let Elga's age be `x`; Alvin's age be `y`

`y-x=12`
is an equation explaining the statement:
'Alvin is 12 years older than Elga'

`x+y=96`
is another equation, which explains the statement:
'The sum of their ages is 96'

from `y-x=12`
`y=12+x`
we form an equation of `y` in terms of `x` as we don't really care much about Alvin's age (`y`).
`y=12+x` will then be substituted into `x+y=96`

Substitution:
`x+(12+x)=96`
`2x=96-12`
`2x=84`
`x=42`

`:.`Elga's age is 42

Answer 2

Elga is `42` and Alvin is `54`

Explanation:

We are working with two people. Write an expression for the age of each. It is easier to use one variable,

Elga is younger, let that age be `x`. Alvin is `12` years older.

Lets Elga's age be `x`
Alvin's age is `x+12`

the sum of their ages is `96`

`x+x+12 = 96" "larr` solve for `x`

`2x +12 =96`

`2x = 96-12`

`2x = 84`

`x = 42`

So, Elga is `42` and Alvin is `54`