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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

Tony is selling boxes of candy for $15 each and T-shirts for $20 each for a fundraiser for his soccer team. Tony's goals are that his total fundraiser sales from these two items will be more than $300, and that he will sell at least as many T-shirts as boxes of candy. Which of the following systems of inequalities best models this situation, where c is the number of boxes of candy and t is the number of T-shirts Tony needs to sell to meet his goals?

A.c+t>300 20t≤15c
B.c+t>300 20t≥15c
C.15c+20t>300 t≥c
D.15c+20t>300 t≤c

答案和解析

答案：C

解析：

Choice C is correct. Tony's first goal is that his total fundraiser sales from 15-dollar boxes of candy and 20-dollar t-shirts will be more than $300. Tony's fundraiser sales can be calculated by (price per T-shirt)*(number of T-shirts sold) + (price per box of candy)*(number of boxes of candy sold). If Tony meets this goal, this value will be greater than $300. This situation can be expressed with the following inequality: 15c+20t＞300.

Tony's second goal is that he will sell at least as many T-shirts as boxes of candy. Therefore, the second inequality should show that the number T-shirts sold, t, is greater than or equal to the number of boxes of candy sold, c. This situation can be expressed with the following inequality: t≥c.

Therefore, the following system of inequalities best models the situation: 15c+20t≤300 t≥c.