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:
You can learn more about the system of linear equations in brainly.com/question/6075514
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