Difference between revisions of "1999 AMC 8 Problems/Problem 17"
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==Problem== | ==Problem== | ||
| − | At | + | At Fat Papa Middle School the 108 students who take the Papa meet in the evening to talk about food and eat an average of two full size, double chocalate, creamy cream cakes apiece. Walter and Gretel are baking Bonnie's Smelliest Bar Cookies 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 cakes. They will make only full recipes, not partial recipes. |
| − | Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough | + | Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cakes? (Some eggs and some cakes may be left over.) |
<math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 15</math> | <math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 15</math> | ||
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==Solution== | ==Solution== | ||
| − | If <math>108</math> students eat <math>2</math> | + | If <math>108</math> students eat <math>2</math> cakes on average, there will need to be <math>108\cdot 2 = 216</math> cakes. There are <math>15</math> cakes per pan, meaning there needs to be <math>\frac{216}{15} = 14.4</math> pans. However, since half-recipes are forbidden, we need to round up and make <math>\lceil \frac{216}{15}\rceil = 15</math> pans. |
<math>1</math> pan requires <math>2</math> eggs, so <math>15</math> pans require <math>2\cdot 15 = 30</math> eggs. Since there are <math>6</math> eggs in a half dozen, we need <math>\frac{30}{6} = 5</math> half-dozens of eggs, and the answer is <math>\boxed{C}</math> | <math>1</math> pan requires <math>2</math> eggs, so <math>15</math> pans require <math>2\cdot 15 = 30</math> eggs. Since there are <math>6</math> eggs in a half dozen, we need <math>\frac{30}{6} = 5</math> half-dozens of eggs, and the answer is <math>\boxed{C}</math> | ||
Revision as of 23:27, 28 October 2016
Problem
At Fat Papa Middle School the 108 students who take the Papa meet in the evening to talk about food and eat an average of two full size, double chocalate, creamy cream cakes apiece. Walter and Gretel are baking Bonnie's Smelliest Bar Cookies 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 cakes. They will make only full recipes, not partial recipes.
Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cakes? (Some eggs and some cakes may be left over.)
Solution
If 
students eat cakes on average, there will need to be 
cakes. There are 
cakes per pan, meaning there needs to be 
pans. However, since half-recipes are forbidden, we need to round up and make 
pans.
pan requires eggs, so pans require 
eggs. Since there are 
eggs in a half dozen, we need 
half-dozens of eggs, and the answer is 
See Also
| 1999 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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. 
