Difference between revisions of "1999 AMC 8 Problems/Problem 19"
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==Solution== | ==Solution== | ||
| − | For <math>216</math> | + | 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> 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! 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 17:11, 11 May 2017
Problem
At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems 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 these items: 
cups flour, 
eggs, 
tablespoons butter, 
cups sugar, and 
package of chocolate drops They will only make full recipes, not partial recipes.
The drummer gets sick. The concert is cancelled. 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 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! 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. 
