Peanuts and Cashews - Equations?

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

I think you asked this question twice. Anyway, I'll answer it this time a different way. (Last time I used the method of substitution.)

0.8P + 0.95C = 12*0.90 = 10.8 (Eq 1)
P + C = 12 (Eq 2)

Let's get Eq 1 into integer form. First, multiply by 100:

80P + 95C = 1080 (Eq 3)

Then divide by 5:

16P + 19C = 216 (Eq 4)

Notice that Eq 4 and Eq 1 are really the same thing. Now take Eq 2 and multiply by 16:

16P + 16C = 16*12 = 192 (Eq 5)

Subtract Eq 5 from Eq 4 to get:

3C = 24 ==> C = 8 (Answer)

and from Eq 2, P = 12 - C = 4 (Answer)

The answer is the same as I got the other time using the method of substitution, but in this problem, the way I did it here is more work. For this problem, the other method was better.

Mostly, because you asked the question twice, you ought to be able to see that lots of times, there are more than one way to do a problem.