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Bruce has $10 in nickels and quarters. The number of nickels is 24 less than twice the number of quarters. How many of each does he have?

 Feb 27, 2020
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Let  n  =  number of nickels.  The value of these nickels is  0.05n.

Let  q  =  number of quarters.  The value of these quarters is 0.25q.

 

The number of nickels is 24 less than twice the number of quarters.   --->   n  =  2q - 24

 

The total value of the nickels and quarters is $10.00.   --->   0.05n + 0.25q  =  10.00

 

Substituting:  0.05(2q - 24) + 0.25q  =  10.00

                       0.10q - 1.20 + 0.25q  =  10.00

                                 - 1.20 + 0.35q  =  10.00

                                              0.35q  =  11.20

                                                     q  =  32                      <---  number of quarters

 

Since  n  =  2q - 24   --->   n  = 2(32) - 24  =  40            <---  number of nickels

 Feb 27, 2020

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