Difference between revisions of "1999 AMC 8 Problems/Problem 17"

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There are 108 people and each gets 2. 2*108 is 216 people. Each recipe makes 15 cookies, so they will have to make 216/15 rounded up cookies witch is 14.4 rounded up which is 15. Then, there are 2 eggs in each recipe so 15*2 = 30 eggs total. Half a dozen is the same as 6 eggs and 30/6=5(c)

Latest revision as of 15:02, 10 November 2019

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 this items: $1\frac{1}{2}$ cups of flour, $2$ eggs, $3$ tablespoons butter, $\frac{3}{4}$ cups sugar, and $1$ package of chocolate drops. 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 cookies? (Some eggs and some cookies may be left over.)

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 15$

Solution

If $108$ students eat $2$ cookies on average, there will need to be $108\cdot 2 = 216$ cookies. There are $15$ cookies per pan, meaning there needs to be $\frac{216}{15} = 14.4$ pans. However, since half-recipes are forbidden, we need to round up and make $\lceil \frac{216}{15}\rceil = 15$ pans.

$1$ pan requires $2$ eggs, so $15$ pans require $2\cdot 15 = 30$ eggs. Since there are $6$ eggs in a half dozen, we need $\frac{30}{6} = 5$ half-dozens of eggs, and the answer is $\boxed{C}$

See Also

1999 AMC 8 (ProblemsAnswer KeyResources)
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

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There are 108 people and each gets 2. 2*108 is 216 people. Each recipe makes 15 cookies, so they will have to make 216/15 rounded up cookies witch is 14.4 rounded up which is 15. Then, there are 2 eggs in each recipe so 15*2 = 30 eggs total. Half a dozen is the same as 6 eggs and 30/6=5(c)

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