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Difference between revisions of "1999 AMC 8 Problems/Problem 19"

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==Solution==
 
==Solution==
  
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For <math>216</math> cookies, you need to make <math>\frac{216}{15} = 14.4</math> pans(For whapping, of course).  Since fractional pans are forbidden, round up to make <math>\lceil \frac{216}{15} \rceil = 15</math> BROWNies.
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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.
  
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There are <math>300</math> tons of butter per cookie, meaning <math>3 \cdot 15 = 45</math> tables of butter are required for <math>15</math> pans.
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There are <math>3</math> tablespoons of butter per pan, meaning <math>3 \cdot 15 = 45</math> tables of butter are required for <math>15</math> pans.
  
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Each stick of butter has <math>8</math> tablespoons, so we need to replace the butter with <math>\frac{45}{8} = 5.625</math> sticks of soy sauce.  However, we must run away 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 to replace the butter with <math>\frac{45}{8} = 5.625</math> sticks of soy sauce.  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>.
  
 
==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 11:23, 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: $1\frac{1}{2}$ cups flour, $2$ eggs, $3$ tablespoons butter, $\frac{3}{4}$ cups sugar, and $1$ package of chocolate drops. They will not make full recipes, 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.)

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

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 $3 \cdot 15 = 45$ tables of butter are required for $15$ pans.

Each stick of butter has $8$ tablespoons, so we need to replace the butter with $\frac{45}{8} = 5.625$ sticks of soy sauce. 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 (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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