2005 AMC 10A Problem 5

Question

A store normally sells windows at

\$100

each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?

100

200

300

400

500

Answer: A

Concepts:money basic counting

Difficulty rating: 1170

Small hint:

Every four windows purchased comes with a fifth window free

Big hint:

Compare buying alone (

7

windows and

8

windows) with buying all

15

together

Solution:

Alone, Dave pays for

6

windows and receives one free to reach

7,

costing

\$600;

Doug pays for

7

and receives one free to reach

8,

costing

\$700.

Separately they pay

\$1300.

Together they need

15

windows: buying

12

yields

3

free, for

\$1200.

The savings are

1300 - 1200 = 100

dollars.

Thus, the correct answer is A.