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We need to determine in how many days Fran and Anne's bird baths will contain the same amount of water. Let's start by setting up equations for each bird bath:

### Fran's Bird Bath:
- Initial amount of water: 8 cups
- Water decreases by \( \frac{1}{3} \) of a cup per day.

The amount of water in Fran's bird bath after \( x \) days can be expressed as:
\[
W_F = 8 - \frac{1}{3}x
\]

### Anne's Bird Bath:
- Initial amount of water: 10 cups
- Water decreases by 1 cup per day.

The amount of water in Anne's bird bath after \( x \) days can be expressed as:
\[
W_A = 10 - 1x = 10 - x
\]

### Step 1: Set the equations equal to each other
To find out when the bird baths will have the same amount of water, set \( W_F = W_A \):
\[
8 - \frac{1}{3}x = 10 - x
\]

### Step 2: Solve for \( x \)
Let's solve this equation step by step.

1. Move all terms involving \( x \) to one side and constants to the other side:
\[
\frac{1}{3}x - x = 10 - 8
\]
\[
\frac{1}{3}x - \frac{3}{3}x = 2
\]

2. Combine like terms:
\[
-\frac{2}{3}x = 2
\]

3. Solve for \( x \):
\[
x = \frac{2}{-\frac{2}{3}} = -2 \times \frac{3}{2} = -3
\]

### Conclusion:
The negative result indicates that, mathematically, Fran’s bird bath already had less water than Anne’s bird bath before the starting point, and they would have had the same amount 3 days earlier.

Would you like more details on any part of this, or do you have any other questions?

Here are some related questions you might find interesting:
1. What would happen if both baths decreased by the same amount each day?
2. How would the problem change if Fran's bath decreased by 1 cup per day?
3. How can this situation be modeled using a graph?
4. What if the rates of decrease changed midway through the scenario?
5. How would the equation change if Fran added water instead of losing it?

**Tip:** When solving word problems, always check if negative results are physically meaningful in the context of the problem!

Fran’s bird bath contains 8 cups of water and decreases by 1/3 of a cup each day. Anne’s bird bath contains 10 cups of water and decreases by 1 cup each day. Write and solve an equation to determine in how many days Fran and Anne’s bird baths will contain the same amount of water.

Learn how to solve this algebra problem involving two bird baths losing water at different rates. Set up and solve linear equations to find when Fran and Anne's bird baths contain the same amount of water. Suitable for students in Grades 6-8.

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