I am a two digit number I am double an odd number my units digit is half my tens digit
"my units digit is half my tens digit"
---> if my unit digit is x, then my tens digit is 2x
if I'm double an odd number then I must be even, and my
unit digit can only be even.
so x = 2 or 4, (x cannot be 6 or more, or else the tens digit would no
longer be a single digit)
if x = 2, then the number is 42, which is twice the odd number 21
if x = 4, then the number is 84, but that is supposed to be twice an odd, which it is not
so the only number possible is 42
Well, well, well, you little two-digit mathematical riddle, you! It seems you want me to find your secret identity, huh? Let's see if I can clown around with the numbers and crack your code!
Okay, so you say you are double an odd number. Well, that means you have to be an even number, my dear. And since your units digit is half your tens digit, it looks like your tens digit should be even too!
So, let's try a little guessing game. How about the number 82? The units digit is 2, which is indeed half of the tens digit 8, and voila, it's an even number!
Now, if my silly guess is incorrect, feel free to tell me, and I'll keep clowning around with the numbers until I get it right!
To solve this problem step-by-step:
Step 1: Let's assume the tens digit as "x" and the units digit as "y".
Step 2: According to the given information, the number is double an odd number. So, we can express this as 2a, where "a" is an odd number.
Step 3: The number is also a two-digit number. Therefore, we can express the number as 10x + y.
Step 4: Combining steps 2 and 3, we can write the equation: 10x + y = 2a.
Step 5: The units digit is half the value of the tens digit. Expressing this as an equation, we have: y = (1/2)x.
Step 6: Substituting the value of y in equation 4, we get: 10x + (1/2)x = 2a.
Step 7: Simplifying the equation from step 6, we have: 20x + x = 4a.
Step 8: Combining like terms in step 7, the equation becomes: 21x = 4a.
Step 9: As "a" is an odd number, we can express it as a = 2b + 1, where "b" is a whole number.
Step 10: Substituting the value of "a" in the equation from step 8, we have: 21x = 4(2b + 1).
Step 11: Distributing on the right side of step 10, we get: 21x = 8b + 4.
Step 12: Simplifying the equation from step 11, we have: 21x - 8b = 4.
Therefore, the equation 21x - 8b = 4 represents the given conditions for a two-digit number that is double an odd number, and the units digit is half the tens digit.
To find the answer, we need to follow the given clues step by step.
1. "I am a two-digit number": This means the number is between 10 and 99.
2. "I am double an odd number": Since the number is double an odd number, it must be an even number itself. Let's call our number "xy".
3. "My units digit is half my tens digit": This means the units digit (y) is half the value of the tens digit (x). Mathematically, we can express this as y = x/2.
Now, let's consider the possible values for the tens digit (x) and find the corresponding units digit (y).
Since the tens digit cannot be zero (as the number is a two-digit number), let's start with x = 1.
If x = 1, then y = 1/2 = 0.5 (not a whole number, so we can discard this value).
If x = 2, then y = 2/2 = 1, which satisfies the condition.
If x = 3, then y = 3/2 = 1.5 (not a whole number).
If x = 4, then y = 4/2 = 2.
If x = 5, then y = 5/2 = 2.5 (not a whole number).
If x = 6, then y = 6/2 = 3 (which is not an odd number, so we can discard this value).
If x = 7, then y = 7/2 = 3.5 (not a whole number).
If x = 8, then y = 8/2 = 4 (which is not an odd number, so we can discard this value).
If x = 9, then y = 9/2 = 4.5 (not a whole number).
So, the only possibility is x = 2 and y = 1. Therefore, the two-digit number that satisfies all the given conditions is 21.