SOLUTION: "Penelope spent all but a nickel of her $10 allowance on chocolate and bubblegum. She bought a total of 4.5 pounds of candy with chocolate costing 3.50/pound and bubblegum costing

Question 831954: "Penelope spent all but a nickel of her $10 allowance on chocolate and bubblegum. She bought a total of 4.5 pounds of candy with chocolate costing 3.50/pound and bubblegum costing .60/pound. How much chocolate and bubblegum did she buy?"
Thank you! x
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
She spent $9.95 on the mixture of candy.

c for pounds of chocolate
b for pounds of bubblegum

c+b=4.5 accounting for pounds of the candy
3.5c+0.6b=9.95 accounting for cost

Modify the cost equation to have all whole numbers.
35c+6b=99.5 ---------- NOT QUITE ALL WHOLE NUMBERS but still useful. This was multiplying left and right by 10.

If you multiply the poundage equation by 6, it becomes 6c+6b=27.

Now look at the way the system is:
6c+6b=27 and 35c+6b=99.5
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Subtract the "27" equation from the "99.5" equation and this eliminates the 6b. You will easily get a value for c. This is the Elimination Method.
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35c+6b-(6c+6b)=99.5-27
29c=72.5
c=2.5 pounds for the chocolate candy
This means b=2.0 pounds of bubblegum
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