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

$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!

Answer 2

`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`