SOLUTION: A bank teller has a bag of change totaling 184.25. The bag contains only quarters and half dollars. If the number of half dollars is 56 more and twice the number of quarters, find

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A bank teller has a bag of change totaling 184.25. The bag contains only quarters and half dollars. If the number of half dollars is 56 more and twice the number of quarters, find       Log On


   

Question 908177: A bank teller has a bag of change totaling 184.25. The bag contains only quarters and half dollars. If the number of half dollars is 56 more and twice the number of quarters, find the number of each type of coin the bag contains
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Answer by AlgebraLady88(44) About Me  (Show Source):
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Quarters and half-dollars have the value of 25 cents and 50 cents each.
The number of half-dollars is 56 more and twice the number of quarters .
This would be written out as:
hd= 2q + 56
To solve :
0.25q + 0.50 hd = 184.25
Since hd= 2q +56
0.25q + 0.50 hd = 184.25
0.25q + 0.50 (2q +56) = 184.25
0.25q + q + 28 = 184.25
1.25 q = 184.25 -28
1.25 q = 156 .25
q = 125
If q= 125 quarters, then to find half-dollars :
hd= 2q + 56
hd= 2(125) + 56
hd= 250 + 56
hd= 306
To check :
125q + 306hd
= 125 ( 0.25) + 306 ( 0.50)
= 31.25 + 153
= 184.25