PSAT Math Multiple-Choice Question 330: Answer and Explanation

Question: 330

A certain student cell phone plan charges $0.10 per text and $0.15 per picture, with no additional monthly fee. If a student sends a total of 75 texts and pictures in one month and is billed $8.90 for that month, how many more texts did he send than pictures?

• A. 19
• B. 28
• C. 36
• D. 47

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Combination

Getting to the Answer: Translate English into math to make sense of the situation. First, define your variables: t for texts and p for pictures are good choices. You know that this student sent a total of 75 texts and pictures. You're also told each text costs $0.10 and each picture is $0.15, and that the bill is $8.90. You'll have two equations: one relating the numbers of texts and pictures and a second relating the costs associated with each:

Multiplying the second equation by 10 allows you to solve for p using combination:

Subtract the second equation from the first to find that -0.5p = -14 and p = 28. But you're not done yet; you're asked for the difference between the text and picture count. Substitute 28 for p in the first equation and then solve for t to get t = 47. Subtracting 28 from 47 yields 19, which is (A).