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
Bill K.
Oct 3, 2015

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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