2004 AMC 10B Problems/Problem 15
Contents
Problem
Patty has coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels, she would have cents more. How much are her coins worth?
Solution 1
She has nickels and dimes. Their total cost is cents. If the dimes were nickels and vice versa, she would have cents. This value should be cents more than the previous one. We get , which solves to . Her coins are worth .
Solution 2
Changing a nickel into a dime increases the sum by cents, and changing a dime into a nickel decreases it by the same amount. As the sum increased by cents, there are more nickels than dimes. As the total count is , this means that there are nickels and dimes.
See also
2004 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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All AMC 10 Problems and Solutions |
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