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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
