Question

1. a coffee shop owner would like to create a blend of cinnamon and hazelnut flavored coffee that sells for $8.00 a pound. currently, the cinnamon coffee sells for $6.00 per pound and the hazelnut coffee sells for $9.00 per pound. which of the following systems of equations could be used to determine the amount , c, in pounds, of the cinnamon flavored coffee, and the amount h, in pounds, of the hazelnut flavored coffee, that should be mixed to obtain 20 pounds of the desired blend?

a. $6c + 9h = 20$
$c + h = 8$
b. $6c + 9h = 8$
$c + h = 20$
c. $6c + 9h = 160$
$c + h = 20$
d. $6c + 9h = 20$
$c + h = 160$

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Explanation:

Step1: Set total weight equation

The total blend is 20 pounds, so the sum of cinnamon ($c$) and hazelnut ($h$) coffee equals 20.
$c + h = 20$

Step2: Set total cost equation

The total cost of the blend is $8.00 \times 20 = 160$ dollars. The cost of cinnamon coffee is $6c$, and hazelnut is $9h$, so their sum equals 160.
$6c + 9h = 160$

Answer:

C. $6c + 9h = 160$
$c + h = 20$