Difference between revisions of "2004 AMC 10B Problems/Problem 15"
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Revision as of 17:50, 24 January 2009
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
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
