I have four digits. I am greater than 11 and less than 12. The sum of the four digits is 13. The digit in the hundredths place is 6. What is the number?
The number is 11.56.
11.__6
1 + 1 + x + 6 = 13
Solve for x
To find the number that satisfies the given conditions, we can break down the information step by step.
1. We know that the number is greater than 11 and less than 12. Since the digit in the hundredths place is 6, the number can be written as 11.6X, where X is the digit in the tenths place.
2. The sum of the four digits is 13. We already know that the digit in the hundredths place is 6. So the sum of the remaining three digits (X + Y + Z, where Y is the digit in the ones place and Z is the digit in the tenths place) must be equal to 13 - 6 = 7.
3. From step 1, we have the equation X + Y + Z = 7.
To find the possible values for X, Y, and Z, we can use trial and error. Since X, Y, and Z are digits, they can only take values from 0 to 9.
Let's consider the possible values for X:
If X = 1, we have 1 + Y + Z = 7. The only possible values for Y and Z that satisfy this equation are Y = 3 and Z = 3 (1 + 3 + 3 = 7). Therefore, one possible number is 11.633.
If X = 2, we have 2 + Y + Z = 7. The only possible values for Y and Z that satisfy this equation are Y = 2 and Z = 3 (2 + 2 + 3 = 7). Therefore, another possible number is 11.623.
If X = 3, we have 3 + Y + Z = 7. The only possible values for Y and Z that satisfy this equation are Y = 1 and Z = 3 (3 + 1 + 3 = 7). Therefore, another possible number is 11.613.
If X = 4, we have 4 + Y + Z = 7. The only possible values for Y and Z that satisfy this equation are Y = 0 and Z = 3 (4 + 0 + 3 = 7). Therefore, another possible number is 11.603.
If X = 5, we have 5 + Y + Z = 7. However, there are no possible values for Y and Z that satisfy this equation, as Y and Z cannot be negative.
So, combining all the information, we have the numbers 11.633, 11.623, 11.613, and 11.603 that satisfy all the given conditions.