the number of my hunderds plus the number of my thousandsin 3. the number of my tens is 7 times the number of my hundreds. the number of my ones is 3 times the number of my thousands. allmy digits are differnt. what number am i ?
The number is abcd
b+a = 3
c = 7b
d = 3a
Since c=7b, b = 0 or 1, or else the product would be > 10
b is not 0, or 7b would also be 0, and all digits are different. S, we now have
a17d
b+a=3, so a = 2:
217d
d=3a, so d=6 and our number is
2176
To find the number that satisfies the given conditions, let's break down the information provided:
1. "The number of my hundreds plus the number of my thousands is 3."
Let's represent the number of hundreds with the variable 'x' and the number of thousands with the variable 'y'. So, according to the given information, we have the equation: x + y = 3.
2. "The number of my tens is 7 times the number of my hundreds."
The number of tens is represented by the variable 'z'. So, we have the equation: z = 7x.
3. "The number of my ones is 3 times the number of my thousands."
The number of ones is represented by the variable 'w'. Thus, we have the equation: w = 3y.
Now, we need to find a solution that satisfies all three equations. Let's solve this system of equations:
From the first equation, we can express 'x' in terms of 'y' by subtracting 'y' from both sides: x = 3 - y.
Substituting this expression for 'x' into the second equation, we have: z = 7(3 - y) = 21 - 7y.
Similarly, substituting the expression for 'y' from the first equation into the third equation, we have: w = 3y.
Now we know that all digits must be different. Since the thousands, hundreds, tens, and ones digits cannot be equal, we can determine that 'y' must be 1, 'x' must be 2, 'z' must be 14, and 'w' must be 3.
Finally, putting all the digits together, the number that satisfies all the given conditions is 2143.
Therefore, the number you are is 2143.