Question

1. the cost of water per gallon varies depending upon where in the state you live. residents in a south georgia city pay $25.50 for 5,000 gallons of water. residents in a north georgia city: a. who would pay more after 15,000 gallons? how much more money would they pay? explain how you know.

Explanation:

Step1: Calculate unit rate for south Georgia city

The unit rate \( r_{south}=\frac{25.50}{5000}= 0.0051\) dollars per gallon.
For 15000 gallons, the cost \(C_{south}=0.0051\times15000 = 76.5\) dollars.

Step2: Calculate unit rate for north Georgia city

We use the first data - point (\(x = 5000\), \(y=46.75\)) to find the unit rate. The unit rate \(r_{north}=\frac{46.75}{5000}=0.00935\) dollars per gallon.
For 15000 gallons, the cost \(C_{north}=0.00935\times15000=140.25\) dollars.

Step3: Find the difference in cost

The difference in cost \(\Delta C=C_{north}-C_{south}\)
\(\Delta C = 140.25 - 76.5=63.75\) dollars.

Answer:

Residents in the north Georgia city would pay more. They would pay \(63.75\) dollars more. We know this by first calculating the unit - rate (cost per gallon) for each city. For the south Georgia city, the unit rate is \(\frac{25.50}{5000}=0.0051\) dollars per gallon, and for 15000 gallons, the cost is \(0.0051\times15000 = 76.5\) dollars. For the north Georgia city, using the first data - point \((5000,46.75)\), the unit rate is \(\frac{46.75}{5000}=0.00935\) dollars per gallon, and for 15000 gallons, the cost is \(0.00935\times15000 = 140.25\) dollars. Then we find the difference \(140.25-76.5 = 63.75\) dollars.