page 19.
A three-digit number has two properties. The tens-digit and the ones-digit add up to 5. If the number is written with the digits in the reverse order, and then subtracted from the original number, the result is 792. Use a system of equations to find all of the three-digit numbers with these properties.
Solution :
The hundred’s digit = x
The tens digit = y
The ones digit = z
y + z = 5 y = 5- z (z is equal or less than 5)
100 * x + 10 * (5-z) + z - 100* z - 10* (5-z) - x = 792
99 * x - 99 * z = 792
x - z = 8
As x can be 8 and 9 only, z would be 0 and 1.
Thus, the three-digit number is 850 or 941