A pet rescue center is creating a monthly food budget. The center currently has two-thirds as many dogs as cats. Each animal is fed 2 cans of food a day. Dog food costs $0.68 per can, while cat food costs $0.65 per can. The rescue center has budgeted a total of $2581.80 for food for this 30-day month. How many dogs are at the rescue center?

Let's solve this problem step by step by defining variables and forming equations based on the given information.

### Step 1: Define the Variables
Let:
- $ C $ represent the number of cats.
- $ D $ represent the number of dogs.

We are told that the rescue center has two-thirds as many dogs as cats. This gives us the relationship:
\[
D = \frac{2}{3}C
\]

### Step 2: Calculate the Total Food Costs for the Animals
- Each dog is fed 2 cans of food per day, and dog food costs $0.68 per can. Therefore, the daily cost for one dog is:
\[
2 \times 0.68 = 1.36 \, \text{dollars/day}.
\]
For a 30-day month, the total food cost per dog is:
\[
30 \times 1.36 = 40.8 \, \text{dollars/month}.
\]

- Each cat is also fed 2 cans of food per day, and cat food costs $0.65 per can. Therefore, the daily cost for one cat is:
\[
2 \times 0.65 = 1.30 \, \text{dollars/day}.
\]
For a 30-day month, the total food cost per cat is:
\[
30 \times 1.30 = 39.0 \, \text{dollars/month}.
\]

### Step 3: Write the Total Budget Equation
The total food budget is $2581.80 for the month. The total cost for all the dogs and cats must add up to this amount. Therefore, the equation for the total cost becomes:
\[
40.8D + 39.0C = 2581.80
\]

### Step 4: Substitute $ D = \frac{2}{3}C $ into the Budget Equation
Now substitute $ D = \frac{2}{3}C $ into the equation:
\[
40.8 \times \frac{2}{3}C + 39.0C = 2581.80
\]
Simplify:
\[
27.2C + 39.0C = 2581.80
\]
\[
66.2C = 2581.80
\]

### Step 5: Solve for $ C $
Solve for $ C $ (the number of cats):
\[
C = \frac{2581.80}{66.2} \approx 39
\]

### Step 6: Solve for $ D $
Now that we know $ C = 39 $, use the relationship $ D = \frac{2}{3}C $ to find the number of dogs:
\[
D = \frac{2}{3} \times 39 = 26
\]

### Final Answer:
There are **26 dogs** at the rescue center.

---

Would you like any additional details or have any questions?

Here are five related questions:
1. How would the budget change if the cost of cat food increased by $0.05 per can?
2. What if the number of dogs was one-half of the number of cats instead?
3. How would the monthly food cost change if each animal ate 3 cans per day instead of 2?
4. What is the cost per animal per day based on this budget?
5. If the budget increased by 10%, how many more dogs or cats could the center feed?

**Tip:** When solving word problems, define variables and set up equations based on relationships described in the problem.

Learn how to calculate the number of dogs at a pet rescue center based on a monthly food budget. This word problem covers key algebraic concepts, including proportions and solving linear equations. Discover how to manage a budget of $2581.80 for 30 days, considering the cost of feeding dogs and cats.

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