I am a number between 400 and 500. My ones digit is 3 more than my tens digit. The sum of my digits is 13. What number am I?
436.
The hundreds must be a four, so the sum of the rest is 13-4=9.
Let x be tens. That gives:
x+(3+x) = 9
x=6
Find ones: 9-6=3.
Amendment (I seem to be doing that a lot when solving problems in my head)
x is, of course 6/2= 3 and represents the tens.
Ones are 9-3=6.
To find the number that satisfies the given conditions, we can break down the problem into steps and reason through each step.
Step 1: Identify the possible values for the tens digit.
Since the tens digit is a single digit number, it can only be between 0 and 9. However, we also know that the ones digit is 3 more than the tens digit. Given this constraint, we can narrow down the possible values for the tens digit.
Let's set up an equation: tens digit + 3 = ones digit.
From the second condition, we know that the sum of the digits is 13.
So, we can express the sum of the digits as: tens digit + ones digit = 13.
Step 2: Solve the equations.
We have two equations:
tens digit + 3 = ones digit
tens digit + ones digit = 13
We can rearrange the first equation to isolate the tens digit:
tens digit = ones digit - 3
Substituting this expression for the tens digit into the second equation:
(ones digit - 3) + ones digit = 13
2 * ones digit - 3 = 13
2 * ones digit = 16
ones digit = 8
Now, substitute the value of ones digit (8) into the first equation to find the value of the tens digit:
tens digit = 8 - 3
tens digit = 5
So, the tens digit is 5 and the ones digit is 8, meaning the number is 58.
Since this number is between 400 and 500, it does not satisfy the given conditions. Thus, there is no number between 400 and 500 that satisfies the given conditions.