Question

Anthony is 5 years older than his sister Ellen, and 7 years ago the sum of their ages was 23 years. In how many years will Anthony be 30 years old?

Answer 1

$\left \{ {{a = e + 5} \atop {(a-7) + (e - 7) = 23} \right.$

a = Anthony
e = Ellen

(e + 5 - 7) + (e - 7) = 23
e + -2 + e - 7 = 23
2e - 9 = 23
Add 9 on both sides.
2e = 32
Divide both sides by 2.
e = 16

a = 16 + 5
a = 21

30 - 21 = 9

In 9 years Anthony will be 30 years old.