Question

How many pounds of peanuts that sell for $1.5 per pound should be mixed with cashews that sell for $4.5 per pound so that a 10-pound mixture is obtained that will sell for $3.00 per pound?

Answer 1

5 pounds of peanuts should be mixed with cashews

Step-by-step explanation:

The given is:

The price of one pound of peanut is $1.5

The price of one pound of cashew is $4.5

10-pound mixture is obtained that will sell for $3.00 per pound

We need to find how many pounds of peanuts should be mixed with cashews

Assume that x represents the number of pound of peanuts, and y represents the number of pounds of the cashews

∵ x pounds of peanuts should be mixed with y pounds of cashews

∵ The mixture obtained is 10 pounds

∴ x + y = 10 ⇒ (1)

∵ The price of each pound of peanut = $1.5

∵ The price of each pound of cashew = $4.5

∴ The selling price of the mixture = 1.5x + 4.5y

∵ The selling price of one pound of mixture = $3

∵ The mixture is 10 pounds

∴ The selling price of the mixture = 3 × 10 = 30

- Equate the two expressions of the selling price of the mixture

∴ 1.5x + 4.5y = 30 ⇒ (2)

Now we have system of equations to solve it

Multiply equation (1) by -4.5 to eliminate y

∵ -4.5x - 4.5y = -45 ⇒ (3)

- Add equations (2) and (3)

∴ -3x = -15

- Divide both sides by -3

∴ x = 5

∵ x represents the number of pounds of peanuts

∴ The number of pound of peanuts is 5

5 pounds of peanuts should be mixed with cashews

Learn more:

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