You have 2 digits, 2 numbers, reverse digits and 54 if the difference and the sum of all is 10
I'm not clear what you're asking, could you clarify what the conditions are for us please?
My grandson came home with the problem that he wrote out on a piece of paper.
He put down that you need a 2 digit, 2 numbers and the difference would be the number 54, and you need to be able to reverse the digits, and the sum of all numbers would add up to the number 10.
We aren't sure if he left something out. That is all we had to go on and cannot figure it out. I know 108 - 54 equals 54, but how do you get 2 digit numbers from that that can be reversed?
Ok, we would need to know the differnece between what and what, e.g., the number - number with digits reversed?
Also, are we adding up the digits?
If this is the case then I think you will find that 82 is the only 2 digit number that meets these requirements.
the answer is 82-28
To solve this problem, let's break down the information given:
1. We need to find two-digit numbers.
2. The difference between these two numbers should be 54.
3. When the digits of each number are reversed, the resulting numbers should also be two-digit numbers.
4. The sum of all the digits in both numbers should equal 10.
Let's start by setting up equations to represent each condition. Let the two-digit numbers be represented as "ab" and "ba," where "a" and "b" represent the tens and units digits, respectively.
1. We need to find two-digit numbers:
a ≠ 0 and b ≠ 0, since zero as the first digit would make it a one-digit number.
2. The difference between these two numbers should be 54:
(10a + b) - (10b + a) = 54
10a + b - 10b - a = 54
9a - 9b = 54
a - b = 6 (divided both sides by 9)
3. When the digits of each number are reversed, the resulting numbers should also be two-digit numbers:
Since a and b are digits, they can only take values from 0 to 9. Thus, we need to ensure that reversing the digits doesn't result in a number greater than 99.
Reversing "ab" gives us "ba," which can be represented as 10b + a.
So, we need to ensure that both 10a + b and 10b + a are less than or equal to 99.
4. The sum of all the digits in both numbers should equal 10:
a + b + b + a = 10
2a + 2b = 10
2a + 2b = 10
a + b = 5 (divided both sides by 2)
Now, let's solve the equations we derived to find the values of a and b:
From equation 3, a - b = 6.
From equation 4, a + b = 5.
Adding these equations together:
(a - b) + (a + b) = 6 + 5
2a = 11
a = 11/2
Since a must be an integer, a cannot be 11/2. Therefore, there are no two-digit numbers that satisfy all the given conditions.
Therefore, it seems that there may be some mistake or missing information in the problem your grandson gave you. Double-check the problem and its conditions to see if there is anything else you might have missed.