Question

Solve the following problem. It may be helpful to use draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit. 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

Answer: 3 pounds of cashews and 7 pounds of peanuts.

Step-by-step explanation:

Let C=cashews

Let P=peanuts

nC + (10-n)P=3.29 x 10

nC + (10-n)P=32.9

C=5.6

P=2.3

5.6n + 2.3(10-n) =32.9

5.6n + 23 - 2.3n = 32.9

3.3n = 9.9

n = 3

10 - n = 7

he needs to mix 3 pounds of cashews and 7 pounds of peanuts.

Answer 2

Below is the solution:

Using 2 equations:
Quantity: c + p = 10 lbs
Value::: 5.6c + 2.3p = 3.29*10 dollars

Multiply thru the Quantity Eq. by 560
Multiply thru the Value Eq. by 100

560c + 560p = 5600
560c + 230p = 3290

Subtract and solve for "p":
330p = 2310
p = 7 lbs (amt. of peanuts needed)

Solve for "c" using c+p = 10
c + 7 = 10
c = 3 lbs (amt. of cashews needed)