A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters does he have?

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A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters does he have?

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Answer 1 · 2015-10-03T03:02:24

The man has 5 dimes and 9 quarters.

Explanation:

This can either be solved by guessing and checking, or by setting up a system of equations. If $d$ is the number of dimes the man has and $q$ is the number of quarters, the fact that he has 14 coins means $d+q=14$ . The fact that he has $$2.75=275$ cents means that $10d+25q=275$ .

$d+q=14\rightarrow d=14-q$

Upon substitution into the second equation, we get

$10*(14-q)+25q=275\rightarrow 140-10q+25q=275$

$\rightarrow 15q=135\rightarrow q=135/15=9$ .

Therefore, $d=14-9=5$ .

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A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters does he have?

1 Answer

Explanation:

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