What percentage of the shirts are $5?

Question

The sales rack at a store has shirts that cost $5, $7, and $9. A shopper buying a shirt from this rack can expect to spend $6.50 on average. 30% of the shirts cost $9. What percentage of the shirts are $5?

Answer 1

30% cost $9, so 70% cost some combination of $5 or $7

percent of $5 shirts is between 0% and 70%

An average of $6.50 means

30(9) + X(5) + (70-X)(7) = 100(6.5) = 650

270 + 5X +490 - 7X = 650

2X = 760-650 = 110

X = 110/2 = 55% are $5 shirts

70-X = 70-55 = 15% are $7 shirts

30% are $9

the weighted average cost of a shirt is

30(9) + 55(5) + 15(7) = 270+275 + 105 = 650 = $6.50 for average shirt cost