Question

The sum of the digits of a three-digit number is 18.

The middle digit is equal to the average of the
remaining two digits. The number formed by
reversing its digits is 198 more than the original
number. What is the number?

Answer 1

567

Explanation:

general number of three digits = 100z + 10y + x

x + y + z = 18
y = (x + z)/2

100x + 10y + z = 198 + 100z + 10y + x

x + y + z = 18

y = (x+ z) / 2

100x - x + z - 100z = 198

x + (x+z)/2 + z = 18

99x - 99z = 198

2x + x + z + 2z = 36

x - z = 2

3x + 3z = 36

x = z + 2

x + z = 12

z + 2 + z = 12

2z = 12 - 2

2z = 10

2/2 z = 10/2

z = 5

x = 5 + 2

x = 7

y = (7+5)/2

y = 12/2

y = 6