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A pound of dried pineapple bits sells for $6.29, a pound of dried banana chips sells for $4.69, and a pound of raisins sells for $2.29. Two pounds of raisins are to be mixed with equal amounts of pineapple and banana to create a trail mix that will sell for $4.49 a pound.

How many pounds of pineapple and banana chips should be used? (Round your answer to the nearest tenth of a pound.)

Answer :

Final answer:

Approximately 1.47 pounds of pineapple and 1.47 pounds of banana chips should be used to create the trail mix.

Explanation:

To solve this problem, we can set up a system of equations based on the given information. Let's denote the weight of pineapple as x pounds and the weight of banana chips as x pounds.

According to the given information, the price per pound of pineapple is $6.29, the price per pound of banana chips is $4.69, and the price per pound of raisins is $2.29.

We know that two pounds of raisins are mixed with equal amounts of pineapple and banana chips to create a trail mix that sells for $4.49 per pound.

Using the concept of weighted averages, we can set up the following equations:

  1. x pounds of pineapple at $6.29 per pound + x pounds of banana chips at $4.69 per pound + 2 pounds of raisins at $2.29 per pound = (x + x + 2) pounds of trail mix at $4.49 per pound
  2. The total weight of the trail mix is x pounds + x pounds + 2 pounds = 2x + 2 pounds

Simplifying the equation, we have:

6.29x + 4.69x + 2(2.29) = (2x + 2)(4.49)

Expanding and simplifying further:

6.29x + 4.69x + 4.58 = 8.98x + 8.98

Combining like terms:

11.98x + 4.58 = 8.98x + 8.98

Subtracting 8.98x from both sides:

3x + 4.58 = 8.98

Subtracting 4.58 from both sides:

3x = 4.40

Dividing both sides by 3:

x = 1.47

Therefore, approximately 1.47 pounds of pineapple and 1.47 pounds of banana chips should be used to create the trail mix.

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Final answer:

We can set up a system of equations based on the given information to find the pounds of pineapple and banana chips needed. Approximately 0.7 pounds of pineapple and banana chips should create the trail mix.

Explanation:

We can set up a system of equations based on the given information to find the number of pounds of pineapple and banana chips needed. Let's assume the amount of pineapple and banana chips used is x pounds each. We know that the total weight of the raisins is 2 pounds, so the importance of the pineapple and banana chips must also be 2 pounds each. The cost of the trail mix per pound is $4.49.

Based on the given prices, the pineapple and banana chips cost $6.29 and $4.69 per pound, respectively. Using the information above, we can create the following equations:

2x + 2(2) = 4.49(2 + x)

6.29x + 4.69x + 2(2) = 4.49(2 + x)

Simplifying the equation gives us:

11.67x + 4 = 8.98 + 4.49x

Subtracting 4.49x from both sides, we get:

7.18x + 4 = 8.98

Subtracting four from both sides, we have:

7.18x = 4.98

Dividing both sides by 7.18, we get the value of x to be approximately 0.69.

Therefore, approximately 0.7 pounds of pineapple and banana chips should be used.

Learn more about trail mix here:

https://brainly.com/question/11767517

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