2014 AMC 12B Problem 1

Problem 1 of 25EasierAlgebra

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?

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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.

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