SOLUTION: A GROCER MIXED GRAPE JUICE AT $2.25 PER GALLON WITH CRANBERRY JUICE AT $1.75 PER GALLON. HOW MANY GALLONS OF EACH SHOULD BE USED TO MAKE 20 GALLONS OF CRANBERRY/GRAPE JUICE WHICH

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Question 124225: A GROCER MIXED GRAPE JUICE AT $2.25 PER GALLON WITH CRANBERRY JUICE AT $1.75 PER GALLON. HOW MANY GALLONS OF EACH SHOULD BE USED TO MAKE 20 GALLONS OF CRANBERRY/GRAPE JUICE WHICH WILL COST $2.10 PER GALLON?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start by assigning variables to the unknown quantities.
Let x = the required number of gallons of grape juice at $2.25 per gallon.
Now, because we want to make a total of 20 gallons of cranberry/grape juice mix, we will need to add (20-x) gallons of cranberry juice at $1.75 per gallon.
At the end we'll have (hopefully) the required 20 gallons of cranberry/grape juice mix at $2.10 per gallon.
Now we can write the equation that will tell us how much of each we will need.
x($2.25)+(20-x)($1.75) = 20($2.10) Simplify and solve for x.
2.25x + 35 - 1.75x = 42 Combine like-terms.
0.5x+35 = 42 Subtract 35 from both sides.
0.5x = 7 Divide both sides by 0.5
x = 14
So we'll need 14 gallons of grape juice @ $2.25 per gallon plus (20-x) 6 gallons of cranberry juice @ $1.75 per gallon to obtain 20 gallons of cranberry/grape juice mix @ $2.10 per gallon.