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algebra senior

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?
(A)
(B)
(C)
(D)
Solution
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.
Final answer
A