word problem

Question

You have one type of chocolate that sells for $2.00/lb and another type of chocolate that sells for $8.30/lb. You would like to have 18.9 lbs of a chocolate mixture that sells for $4.30/lb. How much of each chocolate will you need to obtain the desired mixture?

You will need

_________lbs of the cheaper chocolate
and

_________lbs of the expensive chocolate.

Answer 1

Let x = the number of pounds of the cheaper chocolate

Let y = the number of pounds of the more expensive chocolate

x + y = 18.9       x = 18.9 - y

2x + 8.30y = 4.30(18.9) = 81.27                 Multiply both sides of the equation by 100 to get rid of the decimal points.

200x + 830y = 8127

200(18.9 - y) + 830y = 8127

3780 -200y + 830y = 8127

630y = 4347

y = 6.9 pounds

x = 18.9 - 6.9

x = 12 pounds