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 $d$ $d$ is the number of dimes the man has and $q$ $q$ is the number of quarters, the fact that he has 14 coins means $d + q = 14$ $d+q=14$ . The fact that he has $$ 2.75 = 275$ $$2.75=275$ cents means that $10 d + 25 q = 275$ $10d+25q=275$ .

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

Upon substitution into the second equation, we get

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

$\to 15 q = 135 \to q = \frac{135}{15} = 9$ $\rightarrow 15q=135\rightarrow q=135/15=9$ .

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

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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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