2003 AMC 12B Problem 2

Attempt Problem 2 of the 2003 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs

\$1

more than a pink pill, and Al’s pills cost a total of

\$546

for the two weeks. How much does one green pill cost?

\$7

\$14

\$19

\$20

\$39

Two weeks is

14

days, so find the cost of one day’s pair of pills first

If a green pill costs

g,

then the pink pill costs

g - 1,

and

g + (g-1)

is one day’s cost

Over

14

days the daily cost of the two pills is

\frac{546}{14} = 39.

Let

g

be the cost of a green pill. The pink pill costs

g - 1,

g + (g - 1) = 39,

giving

g = 20.

Thus, the correct answer is D.

Problem 2 in other years