Answer :
Sure! Let's go through this step by step to understand and solve the problem.
### Part (a): Completing the Story
We have the equation [tex]\(20x + 3700 = 25x + 3500\)[/tex], which represents a story about two pools being filled with water. Let's break down what each part of the equation signifies:
1. Pool A:
- Starts with 3700 liters of water.
- Is filled at a rate of 20 liters per minute.
2. Pool B:
- Starts with 3500 liters of water.
- Is filled at a rate of 25 liters per minute.
The equation [tex]\(20x + 3700 = 25x + 3500\)[/tex] shows that, after [tex]\(x\)[/tex] minutes, both pools have the same amount of water.
### Part (b): Solving for [tex]\(x\)[/tex]
Now let's solve [tex]\(20x + 3700 = 25x + 3500\)[/tex] to find the time [tex]\(x\)[/tex] when both pools have the same amount of water.
1. Start with the original equation:
[tex]\[
20x + 3700 = 25x + 3500
\][/tex]
2. Subtract [tex]\(20x\)[/tex] from both sides to bring the terms involving [tex]\(x\)[/tex] to one side:
[tex]\[
3700 = 5x + 3500
\][/tex]
3. Subtract 3500 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
200 = 5x
\][/tex]
4. Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{200}{5} = 40
\][/tex]
So, [tex]\(x = 40\)[/tex]. This means after 40 minutes, both pools will have the same amount of water.
Therefore, the complete parts of the story and solution are:
- (a) Pool A started with 3700 liters of water, and 20 liters per minute. Pool B started with 3500 liters of water, and 25 liters per minute. The amount of water is the same after [tex]\(x\)[/tex] minutes.
- (b) For this equation (and story): [tex]\(x = 40\)[/tex] minutes.
I hope this explanation helps! Let me know if you have any more questions.
### Part (a): Completing the Story
We have the equation [tex]\(20x + 3700 = 25x + 3500\)[/tex], which represents a story about two pools being filled with water. Let's break down what each part of the equation signifies:
1. Pool A:
- Starts with 3700 liters of water.
- Is filled at a rate of 20 liters per minute.
2. Pool B:
- Starts with 3500 liters of water.
- Is filled at a rate of 25 liters per minute.
The equation [tex]\(20x + 3700 = 25x + 3500\)[/tex] shows that, after [tex]\(x\)[/tex] minutes, both pools have the same amount of water.
### Part (b): Solving for [tex]\(x\)[/tex]
Now let's solve [tex]\(20x + 3700 = 25x + 3500\)[/tex] to find the time [tex]\(x\)[/tex] when both pools have the same amount of water.
1. Start with the original equation:
[tex]\[
20x + 3700 = 25x + 3500
\][/tex]
2. Subtract [tex]\(20x\)[/tex] from both sides to bring the terms involving [tex]\(x\)[/tex] to one side:
[tex]\[
3700 = 5x + 3500
\][/tex]
3. Subtract 3500 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
200 = 5x
\][/tex]
4. Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{200}{5} = 40
\][/tex]
So, [tex]\(x = 40\)[/tex]. This means after 40 minutes, both pools will have the same amount of water.
Therefore, the complete parts of the story and solution are:
- (a) Pool A started with 3700 liters of water, and 20 liters per minute. Pool B started with 3500 liters of water, and 25 liters per minute. The amount of water is the same after [tex]\(x\)[/tex] minutes.
- (b) For this equation (and story): [tex]\(x = 40\)[/tex] minutes.
I hope this explanation helps! Let me know if you have any more questions.
