Steve is making bags of mixed nuts. Almonds are $5 per pound & Cashews are $12 per pound. Steve charges $56 per 7 pound bag.

Question

1. Write a system of equations that can be used to determine how many pounds of almonds & how many pounds of cashews Steve uses.

2. Solve the system of equations to determine how many pounds of almonds & cashews Steve uses.

So for #1 I've got it started like this:

A+C = 7
5A + 12C = 56
5(7-C)+12C = 56
35-5C+12C=56

Am I on the right path? Kinda stuck now?

Thanks!

Answer 1

A+C = 7
5A + 12C = 56
5(7-C)+12C = 56
35-5C+12C=56
7C=21
C=3 lbs, A=2lbs

Answer 2

1.X Lbs. of almonds.
Y Lbs. of cashews.
Eq1: x + y = 7
Eq2: 5x + 12y = 56.

2. Multiply Eq1 by -5 and add the Eqs.:
-5x - 5y = -35
+5x + 12y = 56
Sum: 7y = 21
Y = 3 Lbs.
In Eq1, replace Y with 3:
x + 3 = 7
X = 4 Lbs.

Answer 3

Steve is making bags of mixed nuts. Almonds are $5 per pound and cashews are $12 per pound. Steve charges $56 per 7 pound bag.