Question

You have one type of candy that sells for $1.70/lb and another type of candy that sells for $3.40/lb. You would like to have 8.5 lbs of a candy mixture that sells for $2.70/lb. How much of each candy will you need to obtain the desired mixture?
You will need

_____lbs of the cheaper candy
and
______lbs of the expensive candy.

Answer 1

Answer: You will need 3.5lbs of the cheaper candy

and 5 lbs of the expensive candy.

Step-by-step explanation:

Let x represent the number of pounds of the cheaper candy that you would need.

Let y represent the number of pounds of the expensive candy that you would need.

You would like to have 8.5 lbs of a candy mixture. It means that

x + y = 8.5

You have one type of candy that sells for $1.70/lb and another type of candy that sells for $3.40/lb. The candy mixture would sell for $2.70/lb. It means that the total cost of the mixture would be 8.5 × 2.7 = $22.95. The expression would be

1.7x + 3.4y = 22.95- - - - - - - - - - - 1

Substituting x = 8.5 - y into equation 1, it becomes

1.7(8.5 - y) + 3.4y = 22.95

14.45 - 1.7y + 3.4y = 22.95

- 1.7y + 3.4y = 22.95 - 14.45

1.7y = 8.5

y = 8.5/1.7

y = 5

x = 8.5 - y = 8.5 - 5

x = 3.5