SOLUTION: Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value $15.80. The number of quarters was nineteen more th

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Question 1193413: Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value $15.80. The number of quarters was nineteen more than three times the number of dimes. How many quarters and how many dimes did Peter have?
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Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Peter has been saving his loose change for several days.
When he counted his quarters and dimes, he found they had a total value $15.80.
The number of quarters was nineteen more than three times the number of dimes.
How many quarters and how many dimes did Peter have?
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ANSWER. 13 dimes and 58 quarters.


Solution 

x dimes and 19+3x quarters.


Write the money equation

    10x + 25*(19+3x) = 1580  cents.


Simplify and find x

    10x + 25*19 + 75x = 1580

    10x         + 75x = 1580 - 25*19

           85x        =   1105

             x        =   1105/85 

             x        =   13.  


So, there 13 dimes and 19 + 3*13 = 58 quarters.


CHECK.    13*10 + 58*25 = 1580  cents,  total.    ! correct !

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If your mental arithmetic is good, you can solve the problem informally using exactly the same calculations used in the formal algebraic solution shown by the other tutor.

(1) The total value is $15.80
(2) Take away the "extra" 19 quarters. $15.80 - 19($0.25) = $15.80 - $4.75 = $11.05
(3) Group the remaining coins in groups of 3 quarters and 1 dime, each with a total value of 3($0.25)+1($0.10)=$0.85
(4) The number of those groups needed to make the remaining $11.05 is $11.05/$0.85 = 13

So in those 13 groups there are a total of 39 quarters and 13 dimes; now add back in the other 19 quarters to get the final answer of 39+19=58 quarters and 13 dimes.