# Geometry Puzzle – Challenge 71

This is a fun and engaging math puzzle to challenge even the smartest students and help them develop logic skills.

## Challenge:

The total weight of a box and the candies it contains is 12 pounds. After \(\frac{2}{3}\) of the candies are eaten, the box and the remaining candies weigh 5 pounds. What is the weight of the empty box in pounds?

**A-** \(\frac{2}{3}\)

**B-** 1

**C-** \(\frac{3}{2}\)

**D-** \(2\frac{1}{2}\)

**E-** 5

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The correct answer is C.

Let “B” be the weight of the box and “C” be the weight of the candies. So:

B + C = 12

After \(\frac{2}{3}\) of the candies are eaten, the box and the remaining candies weigh 5 pounds. So,

B + \(\frac{1}{3}\) C = 5

Solve the system of two equations:

B + C = 12 → B = 12 – C

B + \(\frac{1}{3}\) C = 5 → 12 – C + \(\frac{1}{3}\) C = 5 → 12 – \(\frac{2}{3}\) C = 5 → C = 10.5

B = 12 – C → B = 12 – 10.5 = 1.5

The weight of the box is 1.5 pounds.

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