Question

The manager of a restaurant found that the cost to produce 100 cups of coffee is ​$63.00​, while the cost to produce 400 cups is ​$213.00. 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 ​$243.00​?

Answer 1

Answer: a. y= 0.5x+13

b. 460 cups of coffee are produced if the cost of production is ​$243.00.

Explanation:

Let x= Number of cups of coffee

y= cost of x cup

a. Let y =mx+c which is a linear equation

According to the question,

`63= 100m+c\ ...(i)`

`213=400m+c\ ...(ii)`

Subtract (i) from (ii), we get

`150=300m\\\\\Rightarrow\ m=(150)/(300)=0.5`

Put value of m in (i), we get

`63=100(0.5)+c\\\\\Rightarrow\ 63=50+c\\\\\Rightarrow c= 63-50=13`

Put value of m and c in the linear equation ,. we get y= 0.5x+13

b. Put y= 243

`243=0.5x+13\\\\\Rightarrow\ 243-13=0.5x\\\\\Rightarrow\ 230=0.5x\\\\\Rightarrow\ x=(230)/(0.5)=(2300)/(5)=460`

Hence, 460 cups of coffee are produced if the cost of production is ​$243.00.