Section B Section B Checkpoint

Problem 1

Lin is making pancakes using a pancake mix and water. In her recipe, the ratio of cups of pancake mix to cups of water is $4 : 3$ .

Lin mixes 20 cups of pancake mix and 15 cups of water. Is this ratio of pancake mix to water equivalent to that in the recipe? Explain your reasoning.
Find two ratios of cups of pancake mix to cups of water to make pancakes that would taste the same as those using the amounts stated in the original recipe. Show your reasoning.

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Solution

Yes. Sample reasoning: Both the cups of pancake mix and the cups of water are 5 times the numbers in the original recipe ( $20 = 5 \boldcdot 4$ and $15 = 5 \boldcdot 3$ ). Lin is making 5 batches of the recipe.
Sample response: $8 : 6$ and $2 : 1\frac{1}{2}$ . The first ratio is for 2 batches of pancakes: $2 \boldcdot 4 = 8$ and $2 \boldcdot 3 = 6$ . The second ratio is for half a batch: 2 is half of 4, and $1\frac{1}{2}$ is half of 3.

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Sample Response

Yes. Sample reasoning: Both the cups of pancake mix and the cups of water are 5 times the numbers in the original recipe ( $20 = 5 \boldcdot 4$ and $15 = 5 \boldcdot 3$ ). Lin is making 5 batches of the recipe.
Sample response: $8 : 6$ and $2 : 1\frac{1}{2}$ . The first ratio is for 2 batches of pancakes: $2 \boldcdot 4 = 8$ and $2 \boldcdot 3 = 6$ . The second ratio is for half a batch: 2 is half of 4, and $1\frac{1}{2}$ is half of 3.