Difference between revisions of "1999 AMC 8 Problems/Problem 19"
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For <math>216</math> cookies, you need to make <math>\frac{216}{15} = 14.4</math> pans. Since fractional pans are forbidden, round up to make <math>\lceil \frac{216}{15} \rceil = 15</math> pans. | For <math>216</math> cookies, you need to make <math>\frac{216}{15} = 14.4</math> pans. Since fractional pans are forbidden, round up to make <math>\lceil \frac{216}{15} \rceil = 15</math> pans. | ||
− | There are <math>3</math> tablespoons of butter per pan, meaning <math>3 \cdot 15 = 45</math> | + | There are <math>3</math> tablespoons of butter per pan, meaning <math>3 \cdot 15 = 45</math> tablespoons of butter are required for <math>15</math> pans. |
Each stick of butter has <math>8</math> tablespoons, so we need <math>\frac{45}{8} = 5.625</math> sticks of butter. However, we must round up again because partial sticks of butter are forbidden! Thus, we need <math>\lceil \frac{45}{8} \rceil = 6</math> sticks of butter, and the answer is <math>\boxed{B}</math>. | Each stick of butter has <math>8</math> tablespoons, so we need <math>\frac{45}{8} = 5.625</math> sticks of butter. However, we must round up again because partial sticks of butter are forbidden! Thus, we need <math>\lceil \frac{45}{8} \rceil = 6</math> sticks of butter, and the answer is <math>\boxed{B}</math>. |
Revision as of 12:24, 8 June 2019
Problem "Doesn't Make Sense"
At Central Middle School the 108 students who take the AMC10 meet in the evening to talk about food and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists this items: cups flour, eggs, tablespoons butter, cups sugar, and package of chocolate drops. They will not make full recipes, not partial recipes.
Walter and Gretel must make enough pans of cookies to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be left over, of course.)
Solution
For cookies, you need to make pans. Since fractional pans are forbidden, round up to make pans.
There are tablespoons of butter per pan, meaning tablespoons of butter are required for pans.
Each stick of butter has tablespoons, so we need sticks of butter. However, we must round up again because partial sticks of butter are forbidden! Thus, we need sticks of butter, and the answer is .
See Also
1999 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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