Question

Blake is 7 years older than Heather. In 7 years the sum of their ages will be 55. How old is Blake now?

Answer 1

24 years old

Explanation:

Let the age of Blake be x and the age of Heather by y then...

x=7+y

7+x+7+y=55

Notice we are adding additional 7s because the question states "in 7 years"

Simplify the second equation...

7+x+7+y=55

14+x+y=55

Subtract 21 from both sides

x+y=41

Solve using substitution (substitute 7+y for x since x = 7+y)

7+y+y=41

Combine like terms

2y+7=41

Subtract 7 from both sides

2y=34

Divide both sides by 2

y=17

x=7+17=24

Blake is 24 years old now