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Algebra / Systems of two linear equations in two variables Difficulty: Medium

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?

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Explanation

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 $3 x minus x$ , 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, $2 x equals 15,000$ . Since $2 x equals 15,000$ , 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.