SOLUTION: A pound of dried pineapple bits sells for $6.19, a pound of dried banana chips sells for $4.29, and a pound of raisins sells for $2.79. Two pounds of raisins are to be mixed with e
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Question 719409: A pound of dried pineapple bits sells for $6.19, a pound of dried banana chips sells for $4.29, and a pound of raisins sells for $2.79. Two pounds of raisins are to be mixed with equal amounts of pineapple and banana to create a trail mix that will sell for $4.99 a pound. How many pounds of pineapple and banana chips should be used? (Round your answer to the nearest tenth of a pound.)
You can put this solution on YOUR website! These mixture problems with money are different from the ones where you have percentages. With these problems we use the fact that the price per pound of the final mixture will be:
(total cost of all the components used to make the mixture)/(total amount of the mixture)
The "total cost of all the components used to make the mixture" would be the sum of the costs of each individual component. In this case it would be the cost of the dried pineapple + the cost of the dried banana chips + the cost of the raisins.
The cost of the dried pineapple will be (the number of pounds of dried pineapple) * (price per pound for the pineapple). In this problem we do not know the number of pounds of dried pineapple. (In fact that is one of the things we are trying to find.) Let's call it "x". So the cost of the pineapple will be:
x * 6.19 or 6.19x
The cost of the dried banana chips will be (the number of pounds of dried banana chips) * (price per pound for the banana chips). In this problem we do not know the number of pounds of dried banana chips. But we are told this this amount is the same as the amount of pineapple. So it will be "x", too, and the cost of the dried banana chips will be:
x * 4.29 or 4.29x
The cost of the raisins will be (the number of pounds of raisins) * (price per pound for the raisins). We're told that we will use 2 pounds of raisins. So the cost of the raisins will be:
2 * 2.79 or 5.58
This makes the total cost of all the components:
6.19x + 4.29x + 5.58
And the total amount of mixture we will end up with will be:
x + x + 2
So the price per pound of our mixture will be:
The price per pound of the mixture is going to be $4.99. So:
We can use this equation to solve the problem.
First we simplify:
Next we can eliminate the fraction by multiplying both sides by 2x+2:
Subtracting 9.98x from each side:
Subtracting 5.58:
Dividing by 0.50 (or multiplying by 2):
Since x was the amount of both the dried pineapple and the dried banana chips, we would use 8.8 pounds of both (plus the 2 pounds of raisins we were told to use) to make a mixture whose price per pound would be $4.99.