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Coin Problems

The key to these problems is to keep the quantity of coins distinct from the value of the coins. An example will illustrate.



Laura has 20 coins consisting of quarters and dimes. If she has a total of $3.05, how many dimes does she have?

(A) 3

(B) 7

(C) 10

(D) 13

(E) 16

Let D stand for the number of dimes, and let Q stand for the number of quarters. Since the total number of coins in 20, we get D + Q = 20, or Q = 20 –– D. Now, each dime is worth 10¢, so the value of the dimes is 10D. Similarly, the value of the quarters is 25Q = 25(20 –– D).

Summarizing this information in a table yields

  Dimes Quarters Total
Number D 20 –– D 20
Value 10D 25(20 –– D) 305


Notice that the total value entry in the table was converted from $3.05 to 305¢. Adding up the value of the dimes and the quarters yields the following equation:

10D + 25(20 –– D) = 305

10D + 500 –– 25D = 305

––15D = ––195

D = 13

Hence, there are 13 dimes, and the answer is (D).

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