Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?

Analyze the question: Mensah is 5. Joyce is three times his age, so Joyce is 15. We need to find how many years from now Joyce's age will be twice Mensah's age.

Concept: Let the number of years be x. Both people age by the same amount, so add x to each age, then set up an equation.

Solution:

• Mensah's age now = 5
• Joyce's age now = 3 × 5 = 15

After x years:

• Mensah = 5 + x
• Joyce = 15 + x

Joyce is twice Mensah's age:

15 + x = 2(5 + x) 15 + x = 10 + 2x 15 − 10 = 2x − x x = 5

Check: In 5 years, Mensah = 10 and Joyce = 20. Since 20 = 2 × 10, this works.

Answer: 5 years, which is option C.

Tip: In age problems, the difference in ages never changes. Here the difference is 10 years. Joyce is twice Mensah's age exactly when Mensah's age equals that difference (10), so Mensah needs to be 10, which is 5 years from now. This shortcut saves time in the exam.