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Chapter 5: Q. 251 (page 658)

In the following exercises, translate to a system of equations and solve.

Marissa wants to blend candy selling for \(1.80 per pound with candy costing \)1.20 per pound to get a mixture that costs her $1.40 per pound to make. She wants to make 90 pounds of the candy blend. How many pounds of each type of candy should she use?

Short Answer

Expert verified

The number of units of $1.80candy is 30 and number of $1.20 candy is 60.

Step by step solution

01

Step 1. Given Information  

The given data is that Marissa wants to blend candy selling for $1.80 per pound with candy costing $1.20 per pound to get a mixture that costs her $1.40 per pound to make. She wants to make 90 pounds of the candy blend.

02

Step 2. Explanation

Let number of pound of $ 1.80 candy be x and number of pound of $1.20 candy be y.

Candy mixture cost is $1.40and total number of units are 90 pounds.

Thus, total value of candy is 90脳$1.40=$126

Total value of candy can be expressed as 1.8x+1.2y=126--(1)

Total units of candy can be expressed as x+y=90--(2)

03

Step 3. Calculation  

Multiply equation (2) with number 1.2and write the revised equation.

1.2(x+y)=1.2(90)1.2x+1.2y=108--(3)

Solve the equation (3) and (1) by subtracting equation (3) from equation (1).

1.8x+1.2y-1.2x-1.2y=216-1080.6x=18x=30

Substitute the value of x in equation (2) to find the value of y.

x+y=9030+y=90y=60

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