Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Luca wants to refill a small pond that lost some water through evaporation. The pond has 10 gallons of water in it before Luca uses a hose to fill it up. The pond fills at a rate of 8 gallons per minute. Suppose that [tex]$y$[/tex] is the amount of water in the pond after [tex]$x$[/tex] minutes. Which equation could be graphed to help Luca find out how much water is in the pond at any time?

A. [tex]$y = 8x + 10$[/tex]
B. [tex][tex]$y = 8x$[/tex][/tex]
C. [tex]$y = 10x + 8$[/tex]
D. [tex]$y = 8x - 10$[/tex]


Sagot :

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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.