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

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?

Exactly 5 ounces

3 ounces more than the amount of yellow paint used in the first batch

1.5 times the amount of yellow paint used in the first batch

1.5 times the amount of blue paint used in the second batch

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Explanation

Choice D is correct. It’s given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch. For any batch of paint that uses the same ratio, the amount of yellow paint used will be $three halves$ , or 1.5, times the amount of blue paint used in the batch. Therefore, the amount of yellow paint Anita will use in the second batch will be 1.5 times the amount of blue paint used in the second batch.

Alternate approach: It’s given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch and that she will use 5 ounces of blue paint for the second batch. A proportion can be set up to solve for x, the amount of yellow paint she will use for the second batch: $2 over 3, equals, 5 over x$ . Multiplying both sides of this equation by 3 yields $2 equals, 15 over x$ , and multiplying both sides of this equation by x yields $2 x equals 15$ . Dividing both sides of this equation by 2 yields $x equals 7 point 5$ . Since Anita will use 7.5 ounces of yellow paint for the second batch, this is $7 point 5 over 5 equals 1 point 5$ times the amount of blue paint (5 ounces) used in the second batch.

Choices A, B, and C are incorrect and may result from incorrectly interpreting the ratio of blue paint to yellow paint used.