An animal shelter $2.35 per day to care for each cats and $5.50 per day to care for each dog. If $89.50 is spent caring for a total of 22 cats and dogs, how much was spent on caring for all of the cats?

Answer

To solve the problem step by step, we will define variables, set up equations based on the information given, and then solve for the amount spent on caring for all the cats.

### Step 1: Define Variables
Let:
- \( x \) = number of cats
- \( y \) = number of dogs

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of cats and dogs is 22:
\[ x + y = 22 \quad \text{(Equation 1)} \]

2. The total amount spent on caring for the cats and dogs is $89.50. The cost per cat is $2.35 and the cost per dog is $5.50. Therefore, the total cost can be expressed as:
\[ 2.35x + 5.50y = 89.50 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 1 into Equation 2
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 22 - x \]

Now, substitute \( y \) into Equation 2:
\[ 2.35x + 5.50(22 - x) = 89.50 \]

### Step 4: Simplify the Equation
Distributing \( 5.50 \):
\[ 2.35x + 121 - 5.50x = 89.50 \]

Combine like terms:
\[ (2.35 - 5.50)x + 121 = 89.50 \]
\[ -3.15x + 121 = 89.50 \]

### Step 5: Isolate the Variable
Subtract 121 from both sides:
\[ -3.15x = 89.50 - 121 \]
\[ -3.15x = -31.50 \]

Now, divide by -3.15:
\[ x = \frac{-31.50}{-3.15} = 10 \]

### Step 6: Calculate the Amount Spent on Cats
Now that we know \( x = 10 \) (the number of cats), we can find the amount spent on caring for all the cats:
\[ \text{Amount spent on cats} = 2.35 \times x = 2.35 \times 10 = 23.50 \]

### Final Answer
The amount spent on caring for all the cats is **$23.50**.

---