Difficult Math Problems

Question

A utility company uses the function C(x) = 0.461x+3; 0<=x<=40

0.283x+10.12; x>40

to calculate the charge, in dollars, for gas customers who use x CCFs in a month.

A. How much would the company charge a customer who used 52 CCFs in a month?

B. How many CCFs did a customer who was charged $22.03 use?

Answer 1

A:

Since 52 > 40, the cost of gas will be given by the expression:

C(x) = 0.283 x + 10.12

substituting x for the given value of 52

C(52) = 0.283 * 52 + 10.12

C(52) = 14.716 + 10.12

C(52) = 24.836

Since the result is a price in Dollars, we should consider only two decimal places, therefor the final answer is:

Answer: $ 24.84

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B:

To determine the amount of CCF that would result in a price of $22.03 , we must solve the expressions for to find the value of x:

First expression:

C(x) = 0.461x + 3

22.03= 0.461x + 3

19.03= 0.461x

19.03/ 0.461 = x

x= 41.280

Since x is greater than 40 , it is outside the range of the expression and does not apply.

Second Expression:

C(x) = 0.283 x + 10.12

22.03= 0.283x + 10.2

11.83= 0.283x

11.83/0.283= x

x= 41.802

In this case, x is greater than 40 so it is valid for the expression, therefor the final answer is:

x= 41.802 CCFs