Question

Chocolates costing $8 per pound are to be mixed with chocolates costing $3 per pound to make a 20 pound mixture. If the mixture is to sell for $5 per pound, how many pounds of each chocolate should be used?

Answer 1

Hello,

Let's assume
x the number of pounds of chcolates costing $8/pound
y the number of pounds of chcolates costing $3/pound


If profits =0
x+y=20==>y=20-x
8*x+3*y=5*(x+y) ==>8*x+3*(20-x)=5(x+20-x)
==>8x+60-3x=100
==>5x=40
==>x=8 and y=20-8=12


Remark:
If we use less chocolates costing $8/pound we will make more profits.

Answer 2

If they sell for $5/pound and you have 20 pounds, that means you'll gain $100 if you sell all of it. So, in order to not go in debt you need you either spend less money than $100 or $100 exactly.

We can make a system of equations to help solve for how many pounds of each we should get:

8x + 3y = 100
x + y = 20

First we want to solve for x in one of the equations:

x = 20 - y

Then we plug that value into the other equation:

8(20 - y) + 3y = 100

Now we simplify everything

160 - 8y + 3y = 100

160 - 5y = 100

Minus 160 on both sides

-5y = 100 - 160

Divide by negative 5 to solve for y

-5y = -60

y = 12

So now we know that we should get 12 pounds of the $3 chocolates. We need 8 more pounds of the $8 chocolates to have a total of 20 pounds.

20 - 12 = 8