Question

Problems $17, 18,$ and $19$ refer to the following:

Cookies For a Crowd

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: $1\dfrac{1}{2}$ cups of flour, $2$ eggs, $3$ tablespoons butter, $\dfrac{3}{4}$ 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.)

$1$

$2$

$5$

$7$

$15$

Solution:

Since the students eat an average of $2$ cookies each, they will eat a total of $108 \cdot 2 = 216$ cookies.

Each recipe makes $15$ cookies, which means we need $\left\lceil\dfrac{216}{15}\right\rceil = 15$ full recipes to make enough cookies.

Each pan requires $2$ eggs, which means we need $15 \cdot 2 = 30$ eggs. There are $6$ eggs in a half-dozen, so we need $30 \div 6 = 5$ half-dozens.

Thus, C is the correct answer.

1999 AMC 8 Problem 17

Solution:

Problem 17 in Other Years