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 butter may be left over, of course.)
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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 stick of butter may be eaten while making the cookies, 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>

Revision as of 18:09, 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: $1\frac{1}{2}$ cups flour, $2$ eggs, $3$ tablespoons butter, $\frac{3}{4}$ cups sugar, and $1$ 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 stick of butter may be eaten while making the cookies, of course.)

$\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 9$

Solution

For $216$ cookies, you need to make $\frac{216}{15} = 14.4$ pans. Since fractional pans are forbidden, round up to make $\lceil \frac{216}{15} \rceil = 15$ pans.

There are $3$ tablespoons of butter per pan, meaning $3 \cdot 15 = 45$ tablespoons of butter is required for $15$ pans.

Each stick of butter has $8$ tablespoons, so we need $\frac{45}{8} = 5.625$ sticks of butter. However, we must round up again because partial sticks of butter are forbidden. Thus, we need $\lceil \frac{45}{8} \rceil = 6$ sticks of butter, and the answer is $\boxed{B}$.

See Also

1999 AMC 8 (ProblemsAnswer KeyResources)
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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