Algebra Puzzle – Challenge 55

Algebra Puzzle – Challenge 55

Who can solve this great math puzzle? This is for smart people who love teasing their brains with math challenges!

Challenge:

Jason’s age is  \(\frac{5}{8}\) of Alice’s age now. In ten years, the sum of Jason’s and Alice’s age will be 72. How old will Alice be in 5 years?

A- 20

B- 30

C- 32

D- 37

E- 42

The Absolute Best Book to challenge your Smart Student!

The correct answer is D.

Let J be the Jason’s age and A be the Alice’s age. Then:
J =\( \frac{5}{8}\) A
In 10 years: (J + 10) + (A + 10) = 72
Replace J with its value in the first equation:
Then: \((\frac{5}{8} A + 10) + (A + 10) = 72 →1 \frac{5}{8} A = 52 → A = 32\)
In 5 years, Alice will be 37. (32 + 5 = 37)

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