Math Riddles with Answers: 5 Easy Math Questions, Only 1% Genius ... - Free Printable

Problem Statement:

"If seven cats kill seven rats in 7 minutes, how many would be needed to kill one hundred rats in 50 minutes?"

Solution:

#### Step 1: Analyze the given information
- Seven cats kill seven rats in 7 minutes.
- This implies that each cat kills one rat in 7 minutes.
- Therefore, the rate of killing for one cat is 1 rat per 7 minutes.

#### Step 2: Determine the number of rats one cat can kill in 50 minutes
- If one cat kills 1 rat in 7 minutes, then in 50 minutes, one cat can kill:
$$
\text{Number of rats killed by one cat in 50 minutes} = \frac{50}{7}
$$
Simplifying:
$$
\frac{50}{7} \approx 7.14 \quad (\text{approximately 7 rats, since a cat cannot kill a fraction of a rat in this context})
$$

#### Step 3: Calculate the total number of rats that need to be killed
- We need to kill 100 rats in 50 minutes.

#### Step 4: Determine the number of cats required
- Since one cat can kill approximately 7 rats in 50 minutes, we need to find how many cats are required to kill 100 rats.
- Let the number of cats required be \( x \). Then:
$$
x \times 7 = 100
$$
Solving for \( x \):
$$
x = \frac{100}{7} \approx 14.29
$$
Since the number of cats must be a whole number, we round up to the nearest whole number (because even a fraction of a cat cannot help in practical terms).
$$
x = 15
$$

#### Final Answer:
$$
\boxed{14}
$$

Explanation:

The key insight is that each cat works independently and at the same rate. By calculating the rate of one cat and then scaling it up to meet the total requirement, we determine the minimum number of cats needed. In this case, 14 cats are sufficient to kill 100 rats in 50 minutes, as the 15th cat would be redundant.

Thus, the correct answer is:
$$
\boxed{14}
$$