2014 AMC 10B Problem 1

Question

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: 560

Small hint:

Translate the nickel condition into an equation for pennies and nickels

Big hint:

Use the total of

13

coins after finding the two counts

Solution:

Let the number of pennies be

p.

Then, the number of nickels is

13-p

and

p-1,

so

13-p=p-1.

This means we have

7

pennies and

6

nickels.

Therefore, the number of cents is

7+6\cdot 5=37.

Thus, the correct answer is C .