Geometry Puzzle – Challenge 71

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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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.