Question

A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.29 per pound. If cashews cost $5.60 per pound and peanuts cost $2.30 per pound, how many pounds of each must he mix?

Answer 1

3 pounds of cashew and 7 pounds of peanuts should be mixed.

Explanation:

Let x be the number of pounds of cashews and y be the number of pounds of peanuts.

∴ Total number of pounds = x + y

According to the question,

x + y = 10 -------(1),

∵ Price of each pound of cashew = $ 5.60,

Price of each pounds of peanuts = $ 2.30,

Also, total price = number of units × price of each units

Thus, total cost = 5.60x + 2.30y,

Since, total pounds = 10, price of each pound of resultant mixture = 3.29,

⇒ Total cost = 3.29 × 10 = 32.9

⇒ 5.60x + 2.30y = 32.9 ------(2)

Equation (2) - 5.60 × equation (1)

⇒ 2.30y - 5.60y = 32.9 - 56

⇒ −3.3y = −23.1

⇒ y = 7

From equation (1),

x + 7 = 10

⇒ x = 10 - 7 = 3.

Hence, 3 pounds of cashew and 7 pounds of peanuts should be mixed.

Answer 2

Let x pounds be the amount of cashews he mixed and y pounds be the amount of peanuts.

1. A grocer wants to make a 10-pound mixture of cashews and peanuts, so x+y=10.
2. If cashews cost $5.60 per pound, then x pounds will cost $5.6x. If peanuts cost $2.30 per pound, then y pounds will cost $2.3y. He can sell the mix for $3.29 per pound, then 10 pounds will cost $32.9 and the second equation is 5.6x+2.3y=32.9

Solve the system

`\left\{\begin{array}{l}x+y=10\\5.6x+2.3y=32.9\end{array}\right.`

of equations:

• from the first equation express x and substitute it into second equation:

`\left\{\begin{array}{l}x=10-y\\5.6(10-y)+2.3y=32.9.\end{array}\right.`

• solve the second equation:

`56-5.6y+2.3y=32.9,\\-3.3y=32.9-56,\\-3.3y=-23.1,\\3.3y=23.1,\\ \\y=(23.1)/(3.3),\\ \\y=7.`

• find x:

`x=10-y=10-7=3.`

Answer: A grocer must take 3 pounds of cashews and 7 pounds of peanuts.