Problem Statement: A two digit number is four times the sum of its digits. How many numbers satisfy the condition?

Solution:

To solve the problem, we need to follow the steps given below:

Step 1: Understand the problem statement

- We are given that a two-digit number is four times the sum of its digits.
- We need to find out how many numbers satisfy this condition.

Step 2: Derive the equation

Let's assume that the tens digit is x and the units digit is y. Hence, the number can be expressed as 10x + y.

According to the problem statement, the number is four times the sum of its digits. Therefore, we can write the following equation:

10x + y = 4(x + y)

Simplifying the equation, we get:

6x = 3y

2x = y

Step 3: Find the numbers that satisfy the condition

To find the numbers that satisfy the given condition, we need to check all possible values of x and y that satisfy the equation 2x = y.

- If x = 1, then y = 2. Therefore, the number is 12.
- If x = 2, then y = 4. Therefore, the number is 24.
- If x = 3, then y = 6. Therefore, the number is 36.
- If x = 4, then y = 8. Therefore, the number is 48.

Step 4: Conclusion

Hence, we have four numbers that satisfy the given condition. They are 12, 24, 36, and 48.

Final Answer: Four numbers satisfy the given condition. They are 12, 24, 36, and 48.