2004 AMC 10B Problem 15

Question

Patty has

20

coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels, she would have

70

cents more. How much are her coins worth?

\$1.15

\$1.20

\$1.25

\$1.30

\$1.35

Swapping raises the value, so she has more nickels than dimes

Each nickel-for-dime swap changes the total by

5

cents

Swapping increases the value, so Patty has more nickels than dimes. Each swapped coin changes the total by

5

cents, so she has

\frac{70}{5} = 14

more nickels than dimes.

With

n + d = 20

and

n - d = 14,

she has

17

nickels and

3

dimes.

Her coins are worth

17 \cdot 5 + 3 \cdot 10 = 115

cents, or

\$1.15.

Thus, the correct answer is A.

Problem 15 in other years