SOLUTION: 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

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.
RELATED QUESTIONS
The manager of a restaurant found that the cost to produce 50 cups of coffee is $... (answered by math_tutor2020)

#24 Marginal Cost of Coffee The manager of a restaurant found that the cost to produce... (answered by stanbon)

Marginal Cost of Coffee. The manager of a restaurant found that the cost to produce 100... (answered by solver91311)

the manager of a nearby cafe found that the cost to produce 100 cups of coffee is $11.02, (answered by Big Poop)

Manager has found that the cost to produce 100 cups of coffee is 11.02 and the cost to... (answered by vksarvepalli)

The manager of a restaurant found that the cost to produce 200 omelets is $186.11, while... (answered by josgarithmetic)

You sell coffee cups at a fair booth. The large cups cost $4, while the small cups cost... (answered by privani)

the amount of coffee cups sold daily at gloria jean's is uniformly distributed with a... (answered by mathmate)

A coffee shop pays Coffee Delivery Company A, a certain price for each disposable cup it... (answered by TimothyLamb)