2004 AMC 12A Problems/Problem 11
- The following problem is from both the 2004 AMC 12A #11 and 2004 AMC 10A #14, so both problems redirect to this page.
Contents
Problem
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is cents. If she had one more quarter, the average value would be cents. How many dimes does she have in her purse?
Solutions
Solution 1
Let the total value, in cents, of the coins Paula has originally be , and the number of coins she has be . Then and . Substituting yields: so , Then, we see that the only way Paula can satisfy this rule is if she had quarters and nickel in her purse. Thus, she has dimes.
Solution 2
If the new coin was worth cents, adding it would not change the mean. The additional cents raise the mean by , thus the new number of coins must be . Therefore there were coins worth a total of cents. As in the previous solution, we conclude that the only way to get cents using coins is . Thus, having three quarters, one nickel, and no dimes
Video Solution
Education, the Study of Everything
Video Solution by OmegaLearn
https://youtu.be/HISL2-N5NVg?t=1649
~ pi_is_3.14
See also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
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 12 Problems and Solutions |
2004 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 |
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