Question

Marissa wants to blend candy selling for $1.40 per pound with candy costing $2.90 per pound to get a mixture that costs her $2.00 per pound to make. She wants to make 30 pounds of the candy blend. How many pounds of each type of candy should she use?

Answer 1

Answer:

30 lb of $1.80 candy

60 lb of $1.20 candy

Step-by-step explanation:

It generally works well to let a variable represent the quantity of the most-expensive contributor. Here, we can let x represent pounds of $1.80 candy.

Then 90-x will be pounds of $1.20 candy, and the total cost of the mix will be ...

 1.80x + 1.20(90-x)

We want that to be the same value as 90 pounds of $1.40 per pound mix, so the equation is ...

 1.80x + 1.20(90 -x) = 1.40(90)

This can be simplified and solved like any two-step linear equation.

 0.60x + 108 = 126 . . . . . simplify

 0.60x = 18 . . . . . . . . . . . .subtract 108

 x = 30 . . . . . . . . . . . . . . . divide by 0.60. This is pounds of $1.80 candy

 90-x = 60 . . . . . pounds of $1.20 candy

30 pounds of candy priced at $1.80 per pound, and 60 pounds of candy priced at $1.20 per pound should be used to make a mix that costs $1.40 per pound.

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Answer 2

Answer: the number of pounds of the $1.40 per pound candy that she would use is 18

the number of pounds of the $2.90 per pound candy that she would use 12

Step-by-step explanation:

Let x represent the number of pounds of the $1.40 per pound candy that she would use.

Let y represent the number of pounds of the $2.90 per pound candy that she would use.

She wants to make 30 pounds of the candy blend. This means that

x + y = 30

If the mixture costs her $2.00 per pound to make, the cost of 30 pounds would be 30 × 2 = $60. The combination of both blends to make the $60 worth mixture is expressed as

1.4x + 2.9y = 60 - - - - - - - - - - - -1

Substituting x = 30 - y into equation 1, it becomes

1.4(30 - y) + 2.9y = 60

42 - 1.4y + 2.9y = 60

- 1.4y + 2.9y = 60 - 42

1.5y = 18

y = 18/1.5

y = 12

x = 30 - y = 30 - 12

x = 18