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Problem-Solving and Data Analysis / Ratios, rates, proportional relationships, and units Difficulty: Medium

Tanya earns $13.50 per hour at her part-time job. When she works z hours, she earns $13 point 5 0 z$ dollars. Which of the following expressions gives the amount, in dollars, Tanya will earn if she works $3 z$ hours?

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Explanation

Choice A is correct. It’s given that when Tanya works z hours, she earns $13 point 5 0 z$ dollars. Since her hourly rate is constant, if she works 3 times as many hours, or $3 z$ hours, she will earn 3 times as many dollars, or $3 times, open parenthesis, 13 point 5 0 z, close parenthesis$ .

Choice B is incorrect. This expression represents adding 3 dollars to the $13 point 5 0 z$ dollars Tanya will earn. Choice C is incorrect. This expression can be rewritten as $16 point 5 0 z$ , which implies that Tanya earns $16.50 per hour, not $13.50. Choice D is incorrect. This expression adds 3 to the number of hours Tanya works, rather than multiplying the hours she works by 3.