Question

How many pounds of almonds priced $5.35 per pound should be mixed with peanuts worth $3.75 per pound in order to obtain 20 pounds of mixture that will sell for $4.50 per pound?

Answer 1

Explanation:

You should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.

Answer 2

• 9.375 pounds of almonds with 10.625 pounds of peanuts

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To solve this problem, we can use a system of equations with two variables:

• x = pounds of almonds at $5.35,
• y = pounds of peanuts at $3.75.

We have two equations based on the given information:

• 1) x + y = 20 (total pounds of the mixture)
• 2) 5.35x + 3.75y = 4.50 * 20 (total cost of the mixture)

Solve the first equation for x:

• x = 20 - y

Substitute the expression for x into the second equation:

• 5.35(20 - y) + 3.75y = 90

Simplify and solve for y:

• 107 - 5.35y + 3.75y = 90
• -1.60y = -17
• y = 10.625

Substitute the value of y back into the expression for x:

• x = 20 - 10.625
• x = 9.375

So, you should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.