Question

A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.15, how many dimes and how many

Answer 1

• 9 dimes and 5 quarters

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Let d be the number of dimes and q be the number of quarters.

We can set up two equations based on the information given:

• d + q = 14 (14 coins in total)
• 0.10d + 0.25q = 2.15 (total value of his change is $2.15)

Use substitution here:

• d = 14 - q (from the first equation)
• 0.10(14 - q) + 0.25q = 2.15 (substituting into the second equation)
• 1.40 - 0.10q + 0.25q = 2.15
• 0.15q = 0.75
• q = 5

So he has 5 quarters.

We can plug that back into either equation to find the number of dimes:

• d + 5 = 14
• d = 9

So he has 9 dimes and 5 quarters.