Question

A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.30, how many dimes and how many

quarters does he have?

Answer 1

8 dimes and 6 quarters

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Work Shown:

d = number of dimes

q = number of quarters

d+q = 14 since this is his coin total; equation solves to d = 14-q

10d+25q = 230 which is the total value in cents

10(14-q)+25q = 230 .... apply substitution rule

140-10q+25q = 230

15q+140 = 230

15q = 230-140

15q = 90

q = 90/15

q = 6 = number of quarters

d = 14-q

d = 14-6

d = 8 = number of dimes

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Check:

8 dimes + 6 quarters = 14 coins

8 dimes = 8*10 = 80 cents

6 quarters = 6*25 = 150 cents

8 dimes + 6 quarters = 80 cents + 150 cents = 230 cents = $2.30

The answers have been confirmed.