Math - In Need of Equation Help?

Question

Suppose that we wish to mix peanuts worth 80 cents per pound with cashews worth 95 cents per pound to obtain 12 pounds of a mixture worth 90 cents per pound. How many pounds of each type of nuts should we use?

P=pounds of peanuts
C=pounds of cashews
Remember to PLEASE work with equations. Showing your work along the way.

Answer 1

0.8P + 0.95C = 12*0.9 = 10.80 (Eq 1)
P + C = 12 (Eq 2)
P = 12 - C (Eq 3)

Substitute this into Eq 1:

0.8(12 - C) + 0.95C = 10.8
9.6 - 0.8C + 0.95C = 10.8
0.15C = 1.2
C = 1.2/0.15 = 120/15 = 8 (Answer)

Substitute into Eq 3:

P = 12 - C = 12 - 8 = 4 (Answer)

Answer 2

OK, start by writing 2 equations
P + C = 12 (12 total pounds)
.80P + .95C = .90 * 12 = 10.8 (value of the cashews and peanuts)

Step 1: Rewrite the first equation to solve for P or C:
P = 12 - C

Step 2: Substitute 12 - C for P in equation #2.
.80P + .95C = 10.8
.80(12-C) + .95C = 10.8
9.6 - .80C + .95C = 10.8
.15C = 1.2
C = 8 lbs
P = 12 - C = 12 - 8 = 4 lbs

Check:
8 lbs Cashews * .95 + 4 lbs Peanuts * .80 = 12 * .90
7.6 + 3.2 = 10.8
10.8 = 10.8 (Correct!)