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Chapter 11: Q. 56 (page 794)

A coffee distributor is blending a new coffee that will cost \(6.90per pound. It will consist of a blend of \)6.00per pound coffee and$9.00 per pound coffee. What amounts of each type of coffee should be mixed to achieve the desired blend?

[Hint: Assume that the weight of the blended coffee is
100pounds.]

Short Answer

Expert verified

The desired blend can be achieved by mixing 70pound of $6.00with 30pound of $9.00.

Step by step solution

01

Step 1. Given

The coffee consist of a blend of $6per pound and $9per pound.

A coffee distributor is blending a new coffee that will cost $6.90

Weight of the blended coffee is 100

02

Step 2. Giving variables.

Let xdenote the amount of coffee needed in $6coffee and ydenotes the amount of coffee needed in $9coffee.

The total amount of coffee is 100

x+y=100y=100-x

Then the equation will be,

6x+9y=6.90(100)6x+9(100-x)=6.90(100)

03

Step 3. Solve the equation.

Solve the above equation,

6x+9(100-x)=6.90(100)6x+900-9x=6909x-6x=900-6903x=210x=70

04

Step 4. Find the other quantity of coffee blend.

Since

y=100-x=100-70=30

Thus 70pound is needed in $6.00coffee and 30pound is needed in $9.00 coffee

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