Question 73620
Let Q equal the unknown number of quarters he has and let D equal the unknown number of dimes.
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Since he has 6 more dimes than quarters we can say that if we added 6 to the number of
quarters that total would be the same as the number of dimes.  In equation form this is:
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{{{Q + 6 = D}}}
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We also know that he has 165 cents total. If we multiply the number of quarters that he has
by 25 cents per quarter that will give us the total number of cents from quarters. In the
same way, if we multiply the number of dimes times 10 cents per dime that will give us
the number of cents from dimes.  Added together the number of cents from quarters and
the number of cents from dimes must total 165.  In equation form this is:
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{{{(25*Q)+(10*D) = 165}}}
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From our first equation we know that D = Q + 6.  Let's substitute Q + 6 for D in the second
equation that talks about cents.  When we do that the second equation becomes:
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{{{(25*Q) + 10*(Q + 6) = 165}}}
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Multiply on the left side to get:
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{{{25*Q + 10*Q + 60 = 165}}}
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Add the two terms containing Q:
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{{{35*Q + 60 = 165}}}
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Eliminate the 60 on the left side by subtracting 60 from both sides of the equation to get:
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{{{35*Q = 105}}}
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Finally divide both sides of this equation by 35 and you get:
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{{{q = 105/35 = 3}}}
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So now we know that we have 3 quarters, just as you said. And since we know that we have
6 more dimes than quarters we know the number of dimes is {{{6+3 = 9}}}.
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There's how you can get the answer of 3 quarters and 9 dimes.
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Hope this helps you to understand how to get the answer by mathematics.