# 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 Oct 3, 2015 #### Answer: 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 $10 d + 25 q = 275$.

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

Upon substitution into the second equation, we get

$10 \cdot \left(14 - q\right) + 25 q = 275 \setminus \rightarrow 140 - 10 q + 25 q = 275$

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

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