1999 AMC 8 Problem 17

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

Answer: C

Concepts:floor and ceiling functions unit conversion

Difficulty rating: 1250

Small hint:

Find how many full recipes are needed for

216

cookies

Big hint:

Each full recipe uses

2

eggs

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.