Question

Pete and his sister, Sophie, play the game Space Mission Commander on their video game

console. Pete has already completed 27 missions. Sophie has only completed 13 missions.
From now on, Pete plans to complete 3 missions per week. Meanwhile, Sophie plans to
complete 5 missions per week.
At some point, Sophie will catch up to Pete. How many weeks will it take? How many
missions each will Pete and Sophie have completed?

Answer 1

It will take 7 weeks for Sophie to catch up to Pete. Both of them will each have completed 48 missions.

Explanation:

27 + 3x = 13 + 5x

27 + 3x - 3x = 13 + 5x - 3x

27 = 13 + 2x

27 - 13 = 13 + 2x - 13

14 = 2x

x = 7

27 + 3x

27 + 3(7)

27 + 21

48

13 + 5x

13 + 5(7)

13 + 35

48