Question

If Rahquez has 14 dimes and quarters in his pocket, and they have a combined value of 215 cents, how many of each coin does he have?

___quarters
___dimes

Answer 1

• 5 quarters
• 9 dimes

Explanation:

You want to know the number of dimes and quarters that together make 215 cents using 14 coins.

Setup

Let q represent the number of quarters (the higher-value coin). Then the number of dimes is (14-q), and the total value in cents is ...

10(14 -q) +25q = 215

Solution

140 +15q = 215 . . . . . simplify

15q = 75 . . . . . . . . . subtract 140

q = 5 . . . . . . . . . . divide by 15

(14 -q) = 9

Rahquez has 5 quarters and 9 dimes.

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Additional comment

You can solve it this way mentally in the following way. Assume all of the coins are dimes. Their value would be 14·10 cents = 140 cents. The actual value of the coins is 215-140 = 75 cents more than that.

Replacing a dime with a quarter adds 15 cents to the value. The difference of 75 cents means that 5 quarters were used (in place of 5 of the dimes). Then the number of dimes is 14-5 = 9.

You will notice that these mental steps match the algebra we used above. The difference of 215 and 140 was found to be 5 times 15 cents.

We can check this by adding the values: 9 dimes is 90 cents; 5 quarters is 125 cents. Added to 90 cents, that gives 215 cents, as we expect.