Question

Two rectangular swimming pools, both measured I meters, are modeled below. What value of y, in meters, would cause the pools to have equal areas?
Responses

6 (y + 3) = 9 y
6 (y + 3) = 9 y EndFragment

3y + 6 = 9 + y
3y + 6 = 9 + y EndFragment

6 (3y) = 9y
6 (3y) = 9y EndFragment

(y + 3) + 6 = 9 + y
(y + 3) + 6 = 9 + y EndFragment
Question 2

Part 2: What is the value of y?

Meters

Answer 1

To find the value of \( y \) that would cause the two rectangular swimming pools to have equal areas, we can start by analyzing the given equations.

1. For the first equation:
\[
6(y + 3) = 9y
\]

2. For the second equation:
\[
3y + 6 = 9 + y
\]

3. For the third equation:
\[
6(3y) = 9y
\]

4. For the fourth equation:
\[
(y + 3) + 6 = 9 + y
\]

It seems that all of these equations are set to find values of \( y \) that equate the areas of the pools.

### Let's solve the first equation:
\[
6(y + 3) = 9y
\]
Expanding the left side:
\[
6y + 18 = 9y
\]
Now, rearranging:
\[
18 = 9y - 6y
\]
\[
18 = 3y
\]
Dividing both sides by 3:
\[
y = 6
\]

### Now let's check the other equations:

**For the second equation:**
\[
3y + 6 = 9 + y
\]
Rearranging gives:
\[
3y - y = 9 - 6
\]
\[
2y = 3
\]
\[
y = \frac{3}{2}
\]

**For the third equation:**
\[
6(3y) = 9y
\]
This simplifies to:
\[
18y = 9y
\]
Subtracting \( 9y \) from both sides gives:
\[
9y = 0
\]
Thus,
\[
y = 0
\]

**For the fourth equation:**
\[
(y + 3) + 6 = 9 + y
\]
Simplifying gives:
\[
y + 9 = 9 + y
\]
So:
\[
0 = 0
\]
This equation is always true, meaning any value of \( y \) satisfies it.

### Conclusion
After solving these equations, the pertinent solutions for \( y \) are \( 6 \) from the first equation, \( \frac{3}{2} \) from the second equation, and \( 0 \) from the third equation. The solution **unique to the first problem statement** is \( \boxed{6} \) meters, as it was designed to find equal area for rectangular swimming pools.