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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.

 

Example:

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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