A proposal for a new library was included on an election ballot. A radio show stated that 3 times as

Question

A proposal for a new library was included on an election ballot. A radio show stated that $3$ times as many people voted in favor of the proposal as people who voted against it. A social media post reported that $15,000$ more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

A.

$7,500$

B.

$15,000$

C.

$22,500$

D.

$45,000$

Accepted Answer

Choice A is correct. It's given that a radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. Let x represent the number of people who voted against the proposal. It follows that 3 x is the number of people who voted in favor of the proposal and 3 x - x , or 2 x , is how many more people voted in favor of the proposal than voted against it. It's also given that a social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Thus, 2 x = 15,000 . Since 2 x = 15,000 , the value of x must be half of 15,000 , or 7,500 . Therefore, 7,500 people voted against the proposal. Choice B is incorrect. This is how many more people voted in favor of the proposal than voted against it, not the number of people who voted against the proposal. Choice C is incorrect. This is the number of people who voted in favor of the proposal, not the number of people who voted against the proposal. Choice D is incorrect and may result from conceptual or calculation errors.

Question a-prop