SOLUTION: A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $19.10 per pound should be mixed with trail mix costing $4.10

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Question 1100734: A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $19.10 per pound should be mixed with trail mix costing $4.10 per pound to create a 31 pound mixture worth $8.94 per pound. (round to the nearest pound)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
31*8.94 =277.14 total
We know the total lbs of the candy. 31
x+y=31
We know that the total cost for the candy is 277.14
19.10*x+4.10*y= 277.14
x=31-y
We substitute for x
19.10*(31-y)+4.10*y= 277.14
We multiply out
592.1-19.10*y+4.10*y= 277.14
We combine like terms.
-15*y=277.14-592.1
-15*y=-314.96
-15*y=-314.96
Isolate y
y=-314.96/-15
y=20.9973333333333 lbs chocolate candy at $ 4.10 $ is-worth $86.0890666666667
Calculate x
x=31-20.9973333333333
x=10.0026666666667 lbs trail candy at $ 19.10 $ is-worth $191.050933333333
We check
19.10*10.0026666666667+4.10*20.9973333333333=277.14
191.050933333333+86.0890666666667=277.14
277.14=277.14
Since 277.14 = 277.14 is TRUE, all is well