The sum of the digits of a three-digit number is 11. If the order of the digits is reversed, the number is decreased by 396. The tens digit is one half of the hundreds digit. Find the number.
The hundreds digit cannot be odd or 8, since 8 + 4 = 12.
Work it from there.
Thank you so much @PsyDAG
To solve this problem, we can set up equations based on the given information.
Let's assume the hundreds digit is represented by 'x', the tens digit by 'y', and the units digit by 'z'.
From the first statement, we know that the sum of the digits is 11. So, we can set up the equation: x + y + z = 11.
According to the second statement, if we reverse the order of the digits, the number is decreased by 396. This can be represented as: 100z + 10y + x - (100x + 10y + z) = 396. Simplifying this equation, we have: 99z - 99x = 396.
Finally, the third statement says that the tens digit is one half of the hundreds digit, so we can write: y = (1/2)x.
Now, we have a system of equations:
1) x + y + z = 11
2) 99z - 99x = 396
3) y = (1/2)x
We can use substitution or elimination method to solve for x, y, and z. Let's use substitution:
From equation 3), we can substitute y in equation 1):
x + (1/2)x + z = 11
Multiplying through by 2 to get rid of the fraction:
2x + x + 2z = 22
3x + 2z = 22
Now, let's substitute y in equation 2):
99z - 99x = 396
99z - 99(2y) = 396
99z - 198y = 396
Dividing through by 99:
z - 2y = 4
z = 4 + 2y
Substituting this value of z into the equation 3):
3x + 2z = 22
3x + 2(4 + 2y) = 22
3x + 8 + 4y = 22
3x + 4y = 14
Dividing through by 2:
(3/2)x + 2y = 7
Now we have a system of equations:
1) 3x + 4y = 14
2) z - 2y = 4
We can solve this system using substitution or elimination method to find the values of x, y, and z.
Alternatively, we can use a computer program or online software to solve this system of equations and find the values of x, y, and z.