The average of a 1 digit number, a 2 digit number and a 3 digit number is 368. What is the smallest possible 1 digit number?
Please help!
A = 1-digit , B = 2-digit , C = 3-digit
A + B + C = 3 * 368 = 1104
999 is largest 3-digit ... 99 is largest 2-digit ... 999 + 99 = 1098
1104 - 1098 = 6
Well, let's see. If we have an average of 368 between a 1-digit number, a 2-digit number, and a 3-digit number, we know that the sum of all three numbers must be 368 times 3, right?
So, let's imagine the smallest possible 1-digit number is just 0. Then, we need to find a 2-digit number and a 3-digit number that add up to 368 times 3.
Let me do some quick calculations. Ah, here we go. The sum of the 2-digit and 3-digit numbers would be 368 times 3 minus 0.
Subtracting the 1-digit number doesn't change the total sum much, so we can just ignore it for now.
Alright, so 368 times 3 is 1104. So, the sum of the 2-digit and 3-digit numbers must be 1104.
The smallest 2-digit number is 10, and the smallest 3-digit number is 100. If we add them together, we'll get 110. And that's not equal to 1104, right?
So, the truth is, there is no 1-digit number that can make the average 368.
Sorry to break it to you. It seems there was a little math trickery going on. But hey, you got a good brain workout in the process!
To find the smallest possible 1-digit number, we need to understand the given information.
Let's assume the 1-digit number is x, the 2-digit number is y, and the 3-digit number is z.
According to the given information, the average of these three numbers is 368:
(x + y + z) / 3 = 368
We know that x is a 1-digit number, which means x can only have the values 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
To find the smallest possible 1-digit number, we can replace x with each of these values and solve the equation to see if it satisfies the condition.
Let's do it step by step:
1. Substitute x = 0 into the equation:
(0 + y + z) / 3 = 368
Simplifying:
y + z = 1104
In this case, there are infinitely many solutions for y and z to satisfy the equation. However, we are looking for the smallest possible 1-digit number, so let's move on to the next step.
2. Substitute x = 1 into the equation:
(1 + y + z) / 3 = 368
Simplifying:
1 + y + z = 1104
y + z = 1103
In this case, y and z should be positive integers, so there are no valid solutions.
3. Continue this process for x = 2, 3, 4, 5, 6, 7, 8, and 9.
After performing the calculations for each value of x, we find that there are no valid solutions in any of these cases.
Therefore, based on the given information, there is no smallest possible 1-digit number that satisfies the condition.
To find the smallest possible 1-digit number in this case, we need to consider the other two numbers.
Let's represent the 1-digit number as x. Since x is a 1-digit number, the possible values for x are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The second number is a 2-digit number, so it will be greater than or equal to 10. Let's represent this number as y.
Finally, since the third number is a 3-digit number, it will be greater than or equal to 100. Let's represent this number as z.
Now, we know that the average of these three numbers is 368. So, we can write the equation as:
( x + y + z ) / 3 = 368
We can rewrite this equation as:
x + y + z = 3 * 368
Now, we need to find the smallest value for x, given that y and z are at least 10 and 100 respectively.
Let's substitute the smallest values for y and z into the equation:
x + 10 + 100 = 3 * 368
Simplifying, we have:
x + 110 = 1104
Subtracting 110 from both sides, we get:
x = 1104 - 110 = 994
Therefore, the smallest possible 1-digit number is 9.
Note: In this scenario, we are assuming that "average" means arithmetic mean.