Question

Randy, Sandy and Todd are my cousins and their combined age is 87 years. Randy is four times as old as Sandy, but Todd is actually 15 years older than Sandy. How old are each of my cousins

Answer 1

Randy is 48 years old

Sandy is 12 years old

Todd is 27 years old

Explanation:

Given

Represent their ages with the first letters of their names:

`R + S + T = 87`

`R = 4 * S`

`T = 15 + S`

Required

Determine their individual ages

We'll solve the above equations using substitution method of simultaneous equations

Substitute 15 + S for T and 4 * S for R in
`R + S + T = 87`

This gives:

`4 * S + S + 15 + S = 87`

`4 S + S + 15 + S = 87`

Collect Like Terms

`4 S + S + S = 87 - 15`

`6S = 72`

Divide through by 6

`S = 72/6`

`S = 12`

This implies that Sandy is 12 years old

Substitute 12 for S in
`R = 4 * S` and
`T = 15 + S`

`R = 4 * 12`

`R = 48`

`T = 15 + 12`

`T = 27`

This implies that Randy is 48 years old and Todd is 27