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?

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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Favouredlyf Favouredlyf · Answer 2 · 2020-02-24T21:55:16+01:00

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