Penuts and cashews mixture problem

Question

A grocer to make a 10 pound mixture of cashews and peanuts that he can sell for $3.29 per pound if cash is cost $5.60 per pound and peanuts cost $2.30 per pound how many pounds of each must he mix?

Answer 1

c represents the amount of cashews

10 - c prepresents the amount of peanuts

5.60c + 2.30(10 - c) = 3.29(10)

Can you solve for c and answer?

Answer 2

Let P = The pounds of peanuts

Let C = The pounds of cashews

The mixture will be a total of 10 pounds so the number of pounds of peanuts plus the number of pounds of cashews will equal 10 pounds. In equation form this is

P + C =10 which we can call equation 1.

The cost of the mixture will be the cost of the peanuts plus the cost of the cashews.

The cost of the peanuts is the number of pounds of peanuts (P) times the cost per pound of peanuts ($2.30) or

cost of peanuts = P*$2.30

Likewise, the cost of the cashews will be the number of pounds of cashews (C) times the cost per pound of cashews ($5.60 per pound).= C * $5.60.

The total cost for the mixture is the cost per pound of the mixture ($3.29) times the total number of pounds of the mixture (10) = 10 * $3.29 = $32.90

Combining these three equations we get

$2.30 P + $5.60 C = $32.90 which we can call equations 2

So now we have two equations and two unknowns that we can solve for the variables.

To solve by substitution we will complete the following steps:

1. Solve one of the equations for one variable in terms of the 2nd variable (in this case solve equation 1 for P)

P + C = 10 --> P = 10 - C

1. Substitute the solution for step 1 into the 2nd equation and solve to the remaining variable.

$2.30 (10 - C) + $ 5.60 C = $32.90

1. This gives us an equation with one variable that we can solve.

$23.00 - $2.30 C + $5.60 C = $32.90

Subtract $23.00 from both sides of the equation and combine like terms.

$3.30 C = $9.90

Divide both sides by $3.30

C = 3 pounds

1. Substitute C back into equation 1 and solve for P

P + C = 10 --> P = 10 - 3 = 7 pounds

1. Check answer by substituting P and C into equation 2.

$2.30 (7) + $ 5.60 (3) = $16.10 + $16.80 = $32.90