Question 991428: the manager at a restaurant found that the cost to produce 150 cups of coffee is $21, while the cost to produce 300 cups of coffee is $36. assume the relationship between the cost y to produce x cups of coffee is linear.
a.) write a linear equation that expresses the cost,y, in terms of the number of cups of coffee,x.
b.) how many cups of coffee are produced if the cost of production is $56?
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! The total cost (y) is the sum of fixed cost (F)
and the cost per cup (C) times the number of cups (x):
.
y=F+Cx
.
First, find C:
y=F+Cx
$21=F+C(150)
F=$21-C(150) Use as F
.
$36=F+C(300)
F=$36-C(300) . Replace F from above.
$21-C(150)=$36-C(300) . Add C(300) to each side.
$21+C(150)=$36 . Subtract $21 from each side.
C(150)=$15
C=$0.10 . Each cup costs $0.10 to produce.
.
Next, find fixed cost (F):
F=$21-C(150)
F=$21-$0.10(150)
F=$21-$15
F=$6 . The fixed cost is $6.
.
(a). The equation:
.
y=F+Cx.
.
y=$6+$0.10x
.
(b). For cost y=$56
.
y=$6+$0.10x
$56=$6+$0.10x
$50=$0.10x
500=x . ANSWER: 500 cups are produced for $56.
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