To determine the correct equation that represents the amount of water in the pond after a certain number of minutes, let's break down the problem step-by-step.
1. Initial Condition:
- The pond initially has 10 gallons of water.
2. Filling Rate:
- The rate at which the pond is being filled is 8 gallons per minute.
3. Formulating the Equation:
- Let [tex]$x$[/tex] be the number of minutes.
- After [tex]$x$[/tex] minutes, the amount of water added to the pond can be calculated as [tex]\(8x\)[/tex] gallons (since water is being added at a rate of 8 gallons per minute).
- Therefore, the total amount of water in the pond after [tex]$x$[/tex] minutes will be the initial amount plus the amount added.
So, we can write the total amount of water [tex]\(y\)[/tex] as:
[tex]\[ y = 10 + 8x \][/tex]
Simplifying this, we get:
[tex]\[ y = 8x + 10 \][/tex]
This equation represents the total amount of water in the pond after [tex]$x$[/tex] minutes.
Therefore, the correct equation from the given options is:
- [tex]$y = 8x + 10$[/tex]
The other options are:
- [tex]$y = 8x$[/tex] (Incorrect because it does not account for the initial 10 gallons)
- [tex]$y = 10x + 8$[/tex] (Incorrect because the rate and initial amount are incorrectly placed)
- [tex]$y = 8x - 10$[/tex] (Incorrect because it subtracts the initial amount rather than adding it)
Thus, the correct equation is:
- [tex]$y = 8x + 10$[/tex]
