SOLUTION: A 14 pound mixture of grapes sells for $3.10. Type 1 grape sells for .25cents a pound and type 2 grape sells for 20 cents a pound. How many pounds of each type were used?

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Question 351969: A 14 pound mixture of grapes sells for $3.10. Type 1 grape sells for .25cents a pound and type 2 grape sells for 20 cents a pound. How many pounds of each type were used?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
create 2 equations since there are two unknowns
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Let A=lbs of type 1 grapes
Let B=lbs of type 2 grapes
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weight equation 1: A+B=14 (together they weight 14 lbs)
Cost equation 2: 0.25A+0.20*B=3.10 (together they cost 3.10)
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multiply equation2 by 100 to eliminate the decimal and work with whole numbers
25A+20B=310
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Solve equation 1 for A: A=14-B
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Substitute into above equation
25*(14-B)+20B=310
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25*14-25B+20B=310 (distribute 25)
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350-5B=310 (combine and simplify)
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-5B=310-350=-40 (sub 350 from both sides)
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B=-40/-5=8
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subsitute B=8 into A=14-B, A=6
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Validate the answer of A=6, B=8 by sub stituting into original equation
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0.25A+0.20*B=3.10
0.25*6+0.2*8=1.5+1.6=3.10 check