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

The first thing we will do for this case is identify variables.
 We have then:
 p = pounds of peanuts
 c = pounds of cashews
 By writing the system we have:
 c + p = 10
 4p + 6.50c = 47.5
 Whose solution is:
 c = 3
 p = 7
 Answer:
 a system of equations that could be used to solve the problem is:
 c + p = 10
 4p + 6.50c = 47.5

Answer 2

p = pounds of peanuts

c = pounds of cashews

c + p = 10

Since the text states the grocer wants to make a 10-pound mixture to sell for 4.75, we can multiply those amounts together to get $47.50 as the total cost.

4p + 6.50c = 47.5

Then using the substitution method, insert the equation; C=10-P into the main equation to find the number of Peanuts needed.

4p+6.50(10-p)=47.50

4p+65-6.50p=47.50

simplify to get:

-2.5p=-17.5

This results in P=7

Then, to find how many pounds of cashews we can insert the equation P=10-C

4(10-C)+6.50c=47.50

40-4c+6.50c=47.50

Then simplify to get:

40+2.5c=47.50

2.5c=7.5

C=3

There will need to be 7 pounds of peanuts and 3 pounds of cashews to complete the desired mix.

The system of equations that could be used to solve the problem could be:

c + p = 10

4p + 6.50c = 47.5