Question

You have one type of chocolate that sells for $6.00/lb and another type of chocolate that sells for $9.70/lb. You would like to have 11.1 lbs of a chocolate mixture that sells for $7.50/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

lbs of the cheaper chocolate => x = 6.6 pounds(Ibs)

lbs of the expensive chocolate => y = 4.5 pounds(Ibs)

Explanation:

Let's the :

lbs of the cheaper chocolate => x

lbs of the expensive chocolate => y

You would like to have 11.1 lbs

Hence:

x + y => 11.1

x = 11.1 - y

You have one type of chocolate that sells for $6.00/lb and another type of chocolate that sells for $9.70/lb. of a chocolate mixture that sells for $7.50/lb.

Hence:

$6.00 × x + $9.70 × y = $7.50 × 11.1

6x + 9.7y = 83.25

Hence, we substitute 11.1 - y for x

6(11.1 - y) + 9.7y = 83.25

66.6 -6y + 9.7y = 83.25

-6y + 9.7y = 83.25 - 66.6

= 3.7y => 16.65

y = 16.65/3.7

y = 4.5 pounds

x = 11.1 - y

x = 11.1 - 4.5

x = 6.6 pounds

Hence:

You will need 4.5 lbs of the cheaper chocolate and 6.6 lbs of