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January 2018
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Alexa was attempting to make muffins with blueberries. Her recipe required 3/4 cup of sugar and 1/8 cup of butter. Alexa accidentally put a whole cup of butter in the mix. Problem:A.
B. This got Alexa wondering how she could remedy similar mistakes if she were to dump in a single cup of some of the other ingredients. Assume she wants to keep the ratios the same.
Solution:A.
1. The ratio of cups of sugar to cups of butter is 3/4 : 1/8. If we multiply both numbers in the ratio by 8, we get an equivalent ratio that involves 1 cup of butter. 8 X 3/4 = 6, and 8 X 1/8 = 1 In other words, In other words, 3/4 : 1/8 is equivalent to 6:1, and so six cups of sugar is needed if there is one cup of butter. 2. In the previous part we saw that we have 8 times as much butter, so all the ingredients need to be increased by a factor of 8 for all the ratios to be the same in the new mixture. 3. The ratio of cups of blueberries to cups of butter is 3/8 : 1/8 in the original recipe, so Alexa will need to add 8 × 3/8 = 3 cups of blueberries to his new mixture. B. 1. The ratio of cups of sugar to cups of blueberries is 3/4 : 3/8. If we multiply both numbers in the ratio by 8/3, we get an equivalent ratio. 8/3 X 3/4 = 2 and 8/3 X 3/8 = 1 Since 3/4 : 3/8 is equivalent to 2 : 1, two cups of sugar is needed if there is one cup of blueberries. 2. The ratio of cups of butter to cups of sugar is 1/8 : 3/4. If we multiply both numbers in the ratio by 4/3, we get an equivalent ratio. 4/3 × 1/8=1/6 and 4/3× 3/4 = 1. In other words, 1/8 : 3/4 is equivalent to 1/6 : 1, and 1/6 cup of butter is needed if there is one cup of sugar. 3. The ratio of cups of blueberries to cups of sugar is 3/8 : 3/4. If we multiply both numbers in the ratio by 4/3, we get an equivalent ratio. 4/3×3/8=1/2 and 4/3×3/4=1. Since 3/8 : 3/4 is equivalent to 1/2:1, Alexa would need 1/2 cup of blueberries if there is one cup of sugar.
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