A three -digit number is equal to seventeen times the sum of the digits. If the digits are reversed the new number is 198more than the original number the sum of extreme digits is 1less than middle digit. Find the original number.
Answers
The original number is 153
Step-by-step explanation:
Let the 3 digits be x, y and z. hence, the original number is 100 x + 10y + z
Based on Condition 1:
The number is 17 times the sum of the 3 digits
Hence ;
100x + 10y + z = 17 (x +y+z)
100 x + 10 y + z = 17 x + 17y + 17 z
Thus;
83 x – 7 y -16z = 0……………………..(1)
Condition 2 of the question states that:
The reverse of the 3 digits was 198 higher than the original number
Thus;
100z + 10y + x = 100 x + 10y + z + 198
99z – 99 x = 198
Dividing by 99
Z – x = 2
Z = 2 + x ………………………….......….(2)
The condition 3 of the question states that
The sum of the extreme digits was 1 less than the middle digits
Thus;
X + z = y -1
Substituting Eq 2 in this equation
X + 2 + x = y – 1
2x – y = -3
Y = 2x + 3 ………………...............… (3)
Substituting the values of y and z in Eq 1
83 x -7 (2x +3) -16 (2+x) = 0
83 x – 14x – 21 -32 – 12x = 0
53 x – 53 = 0
X = 53 / 53 = 1
Y = 2x + 3
= 2 x 1+3
= 5
Z = 2 + x
= 2 + 1
= 3
Thus, the original number is 153