Question

A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use?

Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.

Answer 1

Hope this'll help you.

Answer 2

★ Question :-

• A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use?

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★ Given :-

• Peanuts cost $4.00 per pound
• Cashews cost $6.50 per pound
• Selling Price of mixture $4.75 per pound.
• A grocer wants to make a 10-pound mixture of peanuts an cashews.

★ To find :-

• How many pounds of each should he use?

★ Solution :-

Let p = pounds of peanuts.

Let c = pounds of cashews.

★ Case :- 1

Total amount of mixture = 10 pounds

⟹ p + c = 10

⟹ c = 10 - p .......(1)

★ Case :- 2

Peanuts cost $4.00 per pound

Cashews cost $6.50 per pound

Selling Price of 10 pounds of mixture is $4.75 per pound.

⟹ 4p + 6.5c = 4.75(p + c)

⟹ 4p + 6.5c = 4.75p + 4.75c

⟹ 6.5c - 4.75c = 4.75p - 4p

⟹ 1.75c = 0.75p

⟹ 1.75 × (10 - p) = 0.75 p [using (1)]

⟹ 17.5 - 1.75p = 0.75p

⟹ 17.5 = 1.75p + 0.75p

⟹ 17.5 = 2.5p

⟹ p = 7 ........(2)

Put p = 7 in equation (1), we get

⟹ c = 10 - 7 = 3.

So, it means

7 pounds of peanut ans 3 pounds of cashew are required.