By what percent is the number of 6B pencils sold by Store E less than the…

CONCEPT

When a quantity A is less than a reference quantity B, the percentage decrease is measured relative to B.

If the ratio HB:6B is m:n and the HB count is H, then the 6B count is H × n/m. The percentage decrease is (B − A)/B × 100.

APPLICATION

1. For Store B, HB:6B = 6:5 and the HB count is 480. Therefore, the 6B count is 480 × 5/6 = 400.

2. For Store E, HB:6B = 3:2 and the HB count is 240. Therefore, the 6B count is 240 × 2/3 = 160.

3. The decrease from Store B to Store E is 400 − 160 = 240 pencils.

4. Using Store B as the reference, the percentage decrease is 240/400 × 100 = 60%.

CROSS-CHECK

A 60% decrease from 400 leaves 40% of 400, and 0.40 × 400 = 160, which equals Store E’s 6B-pencil count.

RESULT

Therefore, Store E sold 60% fewer 6B pencils than Store B.