Question

Salma thought of a three-digit number. The digit in the tens place is 6. The digit in the ones place is the digit greater than 8. She added the digit in the hundreds place and the tens place. The sum is the same as the digit in the ones place. What is the digit in the hundreds place?

Answer 1

To find the digit in the hundreds place, we can use an equation based on the given information and solve for the possible values. In this case, the digit in the hundreds place can be either 3 or 5.

Step-by-step explanation:

To find the digit in the hundreds place, we need to make use of the given information. First, we know that the digit in the tens place is 6. Second, we know that the digit in the ones place is greater than 8. Finally, we know that the sum of the digit in the hundreds place and the digit in the tens place is equal to the digit in the ones place.

Let's use a variable to represent the unknown digit in the hundreds place, say 'x'. Using this variable, we can write an equation: x + 6 = digit in ones place.

Since we know the digit in the ones place is greater than 8, we can go through the numbers 9, 10, 11, and so on, substituting them into the equation for 'digit in ones place'. By doing this, we can determine the possible values for 'x' which represents the digit in the hundreds place.

In this case, we find that 'x' can be 3 or 5. Therefore, the digit in the hundreds place can be either 3 or 5.

Answer 2

The digit in the hundreds place is 3.

Let's denote the digits of the three-digit number as follows:

- Hundreds place digit = \(H\)

- Tens place digit = 6

- Ones place digit > 8

The information given can be summarized as follows:

1. The digit in the tens place is 6.

2. The digit in the ones place is greater than 8.

Now, let's consider the statement that Salma added the digit in the hundreds place and the tens place, and the sum is the same as the digit in the ones place. Mathematically, this can be expressed as:

`\[H + 6 = \text{Ones place digit}.\]`

Now, since the ones place digit is greater than 8, let's consider possibilities:

If the ones place digit is 9, then:

`\[H + 6 = 9.\]`

Subtracting 6 from both sides:

`\[H = 3.\]`

So, the digit in the hundreds place is 3.