10. Number Sense Solve this puzzle to find the number of counties in Texas. When this 3-digit number is rounded up to the nearest hundred, it rounds to 300. The digit in the ones place is 4. The sum of the digits in the 3-digit number is 11. What is the number?

Given : When this 3-digit number is rounded up to the nearest hundred, it rounds to 300. The digit in the ones place is 4. The sum of the digits in the 3-digit number is 11.

To find : What is the number?

Solution :

There is a three-digit number.

When this 3-digit number is rounded up to the nearest hundred, it rounds to 300.

i.e. At hundredth place it can be either 2 or 3.

The digit in the ones place is 4.

The sum of the digits in the 3-digit number is 11.

Taking cases :

1) When digit at hundredth place is 2.

The digit in the ones place is 4.

So, The digit at tenth place is 11-4-2=5

The number form will be 254.

2) When digit at hundredth place is 3.

The digit in the ones place is 4.

So, The digit at tenth place is 11-4-3=4

The number form will be 344.