writing equations

Question

Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed $76, while one using 1600 cubic feet was billed $114.

(a) What is the charge in dollars per cubic foot? Give an exact answer.

(b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used. Use lower case w.

(c) How many cubic feet of water used would lead to a bill of $160? Round your answer to the nearest cubic foot.

for part a I got

$19/300

B

19/300w-19

and c

2826.

These answers are wrong but I don't know any other way to solve these different parts. Please explain how you get the correct answer. Thank you!

Answer 1

Gracie, you are on the right track, but 19/300 is not an exact answer. 6 1/3 cents is an exact answer.

 

If you multiply 19/3 by 1000, you'll get 76.33. Multiply by 1600 and you'll get 101.33, meaning your fixed amount is $12.67.

 

160 = (19/3)x + 12.67

147.33 = (19/3)x

x = 147.33(3/19) = 23 gallons.

 

Hope this helps!