Let's break down the problem step by step.
### Part (a):
Question: What is the water bill if a resident of that city uses 40,000 gallons?
1. We know the rate is [tex]$1.33 for 749 gallons.
2. To find out how much it costs for 40,000 gallons, we use a proportion.
Let’s set up our proportion:
\[ \frac{\text{Cost}}{749 \text{ gallons}} = \frac{X}{40000 \text{ gallons}} \]
3. Rearrange to solve for \(X\):
\[ X = \frac{40000 \text{ gallons}}{749 \text{ gallons}} \times 1.33 \text{ dollars} \]
4. Perform the multiplication and division steps:
\[ X = \frac{40000}{749} \times 1.33 \]
This calculation gives us the water bill:
\[ X \approx 71.03 \]
So, the water bill for using 40,000 gallons of water is approximately $[/tex]71.03.
### Part (b):
Question: How many gallons of water can a customer use if the water bill is not to exceed [tex]$130?
1. Again, we use the rate $[/tex]1.33 for 749 gallons.
2. We need to find the maximum gallons [tex]\(G\)[/tex] such that the cost does not exceed [tex]$130.
Set up the proportion:
\[ \frac{1.33 \text{ dollars}}{749 \text{ gallons}} = \frac{130 \text{ dollars}}{G \text{ gallons}} \]
3. Rearrange to solve for \(G\):
\[ G = \frac{130 \text{ dollars}}{1.33 \text{ dollars}} \times 749 \text{ gallons} \]
4. Perform the division and multiplication steps:
\[ G \approx \frac{130}{1.33} \times 749 \]
This calculation gives:
\[ G \approx 73211 \]
So, a customer can use a maximum of approximately 73,211 gallons of water without exceeding a bill of $[/tex]130.
