Question

three-digit number is equal to 17 times the sum of the digits. If the digits an
sed the new number is 198 more than the original number. The sum of
streme digits is 1 less than the middle digit. Find the original number.

Answer 1

Answer:

hope you get your ans

Step-by-step explanation:

Let ones digit = x , tens digit = y , hundreds digit = z

So, number becomes = 100z+10y+x

According to question-

100z+10y+x = 17(x+y+z)

100z+10y+x = 17x + 17y + 17z

100z-17z +10y-17y + x-17x = 0

83z -7y -16x = 0 -----------------------(1)

Also,

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

100z- z +10y-10y +x - 100x +198 = 0

99z - 99x +198 = 0

99x - 99z = 198

x - z = 2

x = z + 2 ----------------------------(2)

And,

z + x = y-1

By putting (2)

y = z+z+2+1

y = 2z+3 ----------------------------(3)

Putting (3) and (2) in (1) we get

83z -7(2z+3) -16(z+2) = 0

83z -14z -21 -16z -32 = 0

53z = 53

z = 1

put z = 1 in (3)

y = 2(1) +3

y = 5

Put z = 1 in (2)

x = 1+3= 3

So. number = 100(1) + 10(5) + 3 = 153

So, number = 153