PSAT Math Multiple-Choice Question 779: Answer and Explanation

Question: 779

The city of Springfield has 50,000 residents ages 15 and 16. Given that the sample in the table is representative of Springfield's residents, approximately how many 15- and 16-year-olds in Springfield would use video chatting as their primary method of electronic communication?

• A. 3,100
• B. 4,870
• C. 8,750
• D. 20,000

Correct Answer: C

Explanation:

(C) Because we are told that the information in the table is representative of the Springfield population, we expect that the fraction of 15- and 16-year-olds in the survey who prefer video chatting will be the fraction of 15- and 16-year-olds in Springfield who prefer video chatting. The fraction in the survey that prefers video chatting is:
= 0.175
Multiplying this decimal by the number of 15- and 16-year-olds in Springfield gives the number of 15- and 16-year-olds in Springfield that we expect to prefer video chatting:
0.175 × 50,000 = 8,750
Choice (C) is correct.
Alternatively, you could have set up a proportion, Let x denote the total number of 15- and 16-year-olds in Springfield who prefer video chatting. Since there are 50,000 15- and 16-year-old residents in Springfield, our proportion is:

By cross multiplying, we get:
3,500,000 = 400x
Dividing both sides by 400 gives:
x = 8,750