Question 59028: A box of coins contains dimes, quarters, and half dollars. The face value of the half dollars and the dimes is the same as the face value of the quarters. Together the face value of the dimes and quarters is $6.50. The total number of coins is 43. How many dimes, quarters, and half dollars are in the box?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A box of coins contains dimes, quarters, and half dollars. The face value of the half dollars and the dimes is the same as the face value of the quarters. Together the face value of the dimes and quarters is $6.50. The total number of coins is 43. How many dimes, quarters, and half dollars are in the box?
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Let # of half dollars be "h"; Value of these is 50h cents
Number of dimes is "d" ; Value of these is 10d cents
Number of quarteris is "q" ; Value of these is 25q cents.
EQUATIONS:
50h+10d=25q
10d+25q=650
h+d+q=43
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I used matrices to get the solution:
Rearrange the equations as follows:
50h+10d-25q=0
0 h+10d+25q=650
h + d + q = 43
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h=5 (number of half-dollars)
d=20(number of dimes)
q=18(number of quarters)
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Cheers,
Stan H.
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