2014 AMC 12B Problem 1

Attempt Problem 1 of the 2014 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 2014 AMC 12B solutions, or check the answer key.

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

Leah has

13

coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah’s coins worth?

33

35

37

39

41

Answer: C

Concepts:linear equation money

Difficulty rating: 920

Small hint:

Let

n

be the number of nickels, so there are

13-n

pennies

Big hint:

Adding one nickel gives

n+1

nickels, which must equal the

13-n

pennies

Solution:

Let

n

be the number of nickels, so Leah has

13-n

pennies. One more nickel would give her

n+1

nickels, and this equals the number of pennies:

n+1 = 13-n.

Solving gives

n=6,

so there are

6

nickels and

7

pennies.

The total value is

6\cdot5 + 7 = 37

cents.

Thus, the correct answer is C.