Difference between revisions of "1999 AMC 8 Problems/Problem 19"
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At Yo Papa Middle School the 108 students who take the Baba meet in the evening to talk about food and eat an average of two cakes apiece. Walter and Gretel are baking nothing this year. Their recipe, which makes a pan of 15 cakes, lists this items: <math>1\frac{1}{2}</math> cups flour, <math>2</math> eggs, <math>3</math> tablespoons butter, <math>\frac{3}{4}</math> cups sugar, and <math>1</math> package of chocolate drops. They will not make full recipes, nor partial recipes. | At Yo Papa Middle School the 108 students who take the Baba meet in the evening to talk about food and eat an average of two cakes apiece. Walter and Gretel are baking nothing this year. Their recipe, which makes a pan of 15 cakes, lists this items: <math>1\frac{1}{2}</math> cups flour, <math>2</math> eggs, <math>3</math> tablespoons butter, <math>\frac{3}{4}</math> cups sugar, and <math>1</math> package of chocolate drops. They will not make full recipes, nor partial recipes. | ||
− | Walter and Gretel must make enough pans to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some sticks of butter may be eaten | + | Walter and Gretel must make enough pans to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some sticks of butter may be eaten in one gulp, of course.) |
<math>\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 9</math> | <math>\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 9</math> | ||
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There are <math>3</math> tablespoons of butter per pan, meaning <math>3 \cdot 15 = 45</math> tablespoons of butter is required for <math>15</math> pans. | There are <math>3</math> tablespoons of butter per pan, meaning <math>3 \cdot 15 = 45</math> tablespoons of butter is 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 | + | 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 since they will be eaten in one gulp. Thus, we need <math>\lceil \frac{45}{8} \rceil = 6</math> sticks of butter, and the answer is <math>\boxed{B}</math>. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=1999|num-b=18|num-a=20}} | {{AMC8 box|year=1999|num-b=18|num-a=20}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 18:17, 29 October 2016
Problem
At Yo Papa Middle School the 108 students who take the Baba meet in the evening to talk about food and eat an average of two cakes apiece. Walter and Gretel are baking nothing this year. Their recipe, which makes a pan of 15 cakes, lists this items: cups flour, eggs, tablespoons butter, cups sugar, and package of chocolate drops. They will not make full recipes, nor partial recipes.
Walter and Gretel must make enough pans to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some sticks of butter may be eaten in one gulp, of course.)
Solution
For cakes, 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 is 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 since they will be eaten in one gulp. 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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