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

Answer:

$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

Answer:

#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#