1) In a survey of cats’ eating habits, 10% of the cats tested showed a clear
preference for Moggiemeat, 20% preferred Fuss-a-Puss and 40% preferred
Yummy Paws. An additional 6 cats did not seem to care at all which of the
three foods they ate, while the remaining 27 cats in the survey would not
touch any of these foods.
How many cats were involved in the survey?
a) 33
b) 63
c) 90
d) 103
e) 110

Let's solve this problem step by step.

### Step 1: Define the given data
- 10% of the cats preferred Moggiemeat.
- 20% of the cats preferred Fuss-a-Puss.
- 40% of the cats preferred Yummy Paws.
- 6 cats did not have a preference.
- 27 cats did not eat any of the three foods.

### Step 2: Calculate the total percentage of cats that showed a preference for the foods
The percentage of cats that showed a preference for any of the foods:
\[ 10\% + 20\% + 40\% = 70\% \]

### Step 3: Let the total number of cats be \( x \)

According to the problem, 70% of the cats prefer one of the three foods:
\[ 0.7x \text{ cats prefer one of the foods.} \]

The remaining 30% of the cats did not have a preference or refused to eat the foods:
\[ 0.3x = 6 \text{ (no preference)} + 27 \text{ (refused all foods)} \]

### Step 4: Solve for \( x \)
\[ 0.3x = 6 + 27 \]
\[ 0.3x = 33 \]
\[ x = \frac{33}{0.3} = 110 \]

So, the total number of cats in the survey is 110.

### Final Answer
The correct answer is **e) 110**.

Would you like more details or have any questions? Here are some related questions:

1. What percentage of the total cats had no preference for any of the foods?
2. How many cats preferred Moggiemeat, Fuss-a-Puss, and Yummy Paws respectively?
3. If the survey included 200 cats, how many would you expect to have no preference?
4. How would the percentages change if 10 more cats refused all foods?
5. What is the probability of randomly selecting a cat that prefers Yummy Paws?

**Tip:** When dealing with percentage problems, always start by assigning a variable to the total amount, and express everything else in terms of that variable.

Solve a survey problem on cats' eating habits. Learn how to determine the total number of cats involved in the survey based on their food preferences. This problem involves percentages and data analysis. Suitable for students in Grades 6-8.

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