Question 193721: The owners of a candy store want to sell, for $5 per pound, a mixture of chocolate-covered raisins, which usually
sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound. They have
a 50 pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of raisins so that
they hit their target value of $5 per pound for the mixture?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the required number of pounds of macadamia nuts at $8.00 per pound.
These will be mixed with the 50 pounds of chocolate-covered raisins (mmmm) at $3.00 per pound.
The final result will be (50+x) pounds of mixture at $5.00 per pound.
So, putting it all together, we get the cost of the 50 pounds chocolate-covered rains is $3.00(50) and the cost of the x pounds of macadamia nuts is $8.00(x) and the sum of these two will be (x+50) pounds of the mixture at $5.00 per pound. Let's write the equation to solve for x.
3(50)+8(x) = 5(50+x) Simplify.
150+8x = 250+5x Subtract 5x from both sides.
150+3x = 250 Subtract 150 from both sides.
3x = 100 Divide both sides by 3.
x = 33.33
So the candy store owners will need to mix 33 1/3 pounds of macadamia nuts (at $8.00 per pound) with the 50 pounds of chocolate-covered raisins (at $3.00 per pound) to obtain 83 1/3 pounds of mixture at $5.00 per pound.
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