Question

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

Answer 1

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!

Answer 2

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