Alex is x years old. June is 7 years older than Alex. In 5 years, their total combined age will be 31 years.

Answer: Alex is 7 years old.

June is 14 years old.

Form your equations. Let x be Alex's age. Let y be June's age.

x + 7 = y

(x + 5) + (y + 5) = 31

Isolate x in the first equation.

x + 7 = y Subtract 7 from both sides

x = y - 7 Isolated x!

Substitute in (y - 7) for x in the second equation.

[ (y - 7) + 5] + (y + 5) = 31 Distributive Propert

y - 7 + 5 + y + 5 = 31 Combine like terms

2y - 7 + 5 + 5 = 31 Combine like terms

2y + 3 = 31 Subtract 3 from both sides

2y = 28 Divide by 2 to both sides

y = 14 Answer!

Substitute in (14) for y in the first equation.

x = 14 - 7 Simplify

x = 7 Answer!

Let Alex's age is x and June's age is y y - x = 7 ... (1)

(x+5) + (y+5) = 31

x + y = 21 ... (2)

by adding 1 and 2

2y = 28

y = 14

x = 7