The manager of a restaurant found that the cost to produce 150 cups of code is $48.50, while the cost to produce 250 cups is $73.50. As

Question

The manager of a restaurant found that the cost to produce 150 cups of code is $48.50, while the cost to produce 250 cups is $73.50. 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 $118.50?

Answer 1

73.50 - 48.50 = $25 for 250 - 150 = 100 cups

1 cup costs 25/100 = 25 cents

150 cups times 25 cents = 150(.25) = $37.50= variable cost

48.50 = 37.50 = $11 fixed cost

y = .25x + 11 = variable cost + fixed cost = total cost

118.50 = y = .25x +11

.25x = 118.50 -11 = 107.5

x = 107.5/.25 = 4 times 107.5 = 430 cups

Answer 2

73.50 - 48.50 = 25/100 cups = 1/4cups  Thats .25 per cup

150 x .25 = 37.50

48.50 - 37.50 = 11 (fixed cost

y = .25x + 11

 

118.50 = .25x + 11

107.50 = .25x

x = 430 cups of coke