PSAT Math Grid-Ins Question 27: Answer and Explanation

Question: 27

A theater sells student tickets to a play for $24 and regular admission tickets for $36. If the theater sells out the 100-seat theater for opening night and has total ticket sales of $3,144, how many of the tickets sold were student tickets?

Correct Answer: 38

Explanation:

38

The question asks for the number of student tickets that were sold. Use Bite-Sized Pieces to translate from English to math and then solve the resulting system of equations. Let s represent the number of student tickets sold and r represent the number of regular tickets sold. Since the 100-seat theater sold out, s + r = 100. Student tickets are $24, regular admission tickets are $36, and total ticket sales are $3,144, so 24s + 36r = 3,144. The question asks for the number of student tickets sold, so solve for s. Start with the first equation. Subtract s from both sides to get r = 100 - s. Substitute this value of r into the second equation to get 24s + 36(100 - s) = 3,144. Distribute the 36 to get 24s + 3,600 - 36s = 3,144. Combine like terms on the left side by subtracting to get -12s + 3,600 = 3,144. Subtract 3,600 from both sides to get -12s = -456. Divide both sides by -12 to get s = 38. The correct answer is 38.