S95-19

Official Solution:

In a certain shipment of T-shirts, 20 percent are red. Of those shirts, 30 percent are size small. If there are 366 red, small T-shirts, how many T-shirts in total were in the original shipment?

A. 732
B. 1220
C. 1830
D. 4806
E. 6100


We are trying to find \(t\), the total number of T-shirts in the original shipment. The problem says that \(20%\) of these T-shirts are red. Recall that the word "of" entails multiplication, so we can represent the number of red T-shirts as \(20% \times t\). Converting the percent to a decimal, we get: \(0.2t\).

Of these red shirts, \(30%\) are small, so the number of small T-shirts is \(30% \times 0.2t = 0.3(0.2t)\). Since there are 366 of these red, small T-shirts, we can formulate the equation: \(0.3(0.2t) = 366\).

Now we solve for \(t\), the number of total T-shirts in the shipment. \(0.3(0.2) = 0.06\), so \(0.06t = 366\). Since \(0.06 = \frac{6}{100} = \frac{3}{50}\), we have \(\frac{3}{50} \times t = 366\). Multiplying both sides by \(\frac{50}{3}\), we get \(\frac{50}{3}(0.06t) = 366 \times \frac{50}{3}\), so \(t = 366\leftarrow(\frac{50}{3}\rightarrow)\). To avoid large numbers, we divide by 3 first: \(t = 366 \times \frac{50}{3} = 122 \times 50 = 6100\).


Answer: E