1983 AMC 12 Problem 7

Attempt Problem 7 of the 1983 AMC 12 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 1983 AMC 12 solutions, or check the answer key.

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

Alice sells an item at

\$10

less than the list price and receives

10\%

of her selling price as her commission. Bob sells the same item at

\$20

less than the list price and receives

20\%

of his selling price as his commission. If they both get the same commission, then the list price is

\$20

\$30

\$50

\$70

\$100

Let

L

be the list price and write each commission in terms of

L

Set

0.1(L-10)

equal to

0.2(L-20)

If the list price is

L,

equality of commissions gives

0.1(L-10)=0.2(L-20).

Multiplying by

10

and solving gives

L-10=2L-40,

L=30.

Therefore, the correct answer is B.

Problem 7 in other years