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?
- 3
- 7
- 10
- 13
- 16
Solution
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 â€“ D.
Now, each dime is worth 10Â¢, so the value of the dimes is 10D.
Similarly, the value of the quarters is 25Q = 25(20 â€“ D).
Summarizing this information in a table yields
Dimes | Quarters | Total | |
Number | D | 20 â€“ D | 20 |
Value | 10D | 25(20 â€“ D) | 305 |
10D + 25(20 â€“ D) = 305
10D + 500 â€“ 25D = 305
â€“15D = â€“195
D = 13
Hence, there are 13 dimes, and the answer is (D).