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?

2 Answers
Aug 4, 2017

$8 chocolate = 8
$3 chocolate = 12

Explanation:

So we need to set up an equation for the information we have.
I'll be using simultaneous equations.

$8 chocolate = x
and
$3 chocolate = y
So, Equation 1 :

x pounds + y pounds = 20 pounds
x + y = 20

And equation 2:

($8 times x pounds) + ($3 times y pounds) = 20 pounds times $5
8x + 3y = 100

Now we need to take equation 1 and make x the subject

x = 20 - y

Now we need to sub that into equation 2 to get

8(20 -y) + 3y = 100

Simplify to get

160 - 8y + 3y = 100

-8y + 3y = 100 - 160

-5y = -60

y = (-60)/-5

y = 12

Now we sub that into equation 1 with x as the subject

x = 20 - 12

x = 8

Hope this helped!

Aug 4, 2017

8 pounds of $8 chocs and 12 pounds of $3 chocs.

Explanation:

Set up a system of equations.

Let the number of $8 pounds be x and
the number of $3 pounds be y
There will be 20 pounds altogether.

x+y =20" " rArr y = (20-x)

The value of the $8 chocs will be: 8x
The value of the $3 chocs will be 3y
The total value of the chocs will be 20 xx 5 =100

8x +3y =100

Now you can solve the two equations:

8x +3(20-x) = 100" "larr subst for y

8x +60-3x = 100

5x = 100-60

5x = 40

x =8
y=12

8 pounds of $8 chocs and 12 pounds of $3 chocs.

Check: 8 xx 8 +12 xx 3 = 64+36 =100