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

@Elijah16

Answer 2

OK i know one equation would be 4x+6.5y=4.75 but what is the second equation

Answer 3

@a1234

Answer 4

The other equation is p + c = 10.

Answer 5

P = 7
C = 3

Answer 6

thanks both of you

Answer 7

You're welcome.

Answer 8

you are super helpful

Answer 9

Write an equation for the total weight.
p + c = 10

Write an equation for the mixture. Remember the final mixture is $4.75 for each of 10 lbs so multiply 4.75 x 10:
4.00p + 6.50c = 4.75(10)

Let's simplify the second equation:
4p + 6.5c = 47.5

Multiply both sides by 2 to get rid of the decimals:
8p + 13c = 95

Then solve the first equation for one variable (say p):
p = 10 - c

Substitute:
8(10-c) + 13c = 95

Distribute the 8 through the parentheses:
80 - 8c + 13c = 95
80 + 5c = 95

Subtract 80 from both sides:
5c = 15

Divide both sides by 5:
c = 15/5
c = 3

Then substitute back to get p:
p = 10 - c
p = 10 - 3
p = 7

Answer:
7 lbs of peanuts
3 lbs of cashews

Source: Yahoo