Question

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number,

the digits are interchanged. The addition of first and third digit is 1 less than middle digit.

Find the number.

Answer 1

You have told me that a number a|b|c is true for these statements

100a+10b+c=17a+17b+17c100a+10b+c+198=100c+10b+aa+c=b-1

I will look at equation 2, removing 10b from both sides

100a+c+198=100c+a

99a+198–99c=0

99(a+2-c)=0

a+c-2=0

a+2=c

Now I will take that information and apply it to equation 3

a+a+2=b-1

b=2a+3

Now I will enter this, with the information I got from equation 2, into equation 1

100a+10(2a+3)+(a+2)=17a+17(2a+3)+17(a+2)

I will distribute

100a+20a+a+30+2=17a+34a+17a+51+34

And combine like terms

121a+32=68a+85

53a=53

a=1

SO, let’s solve for b

2a+3=b

2+3=b

b=5

SO, let’s solve for c

a+2=c

1+2=c

c=3

SO, the number is  153

(I could be totally wrong, really)

(Let’s see!)

1+5+3=9

9*17=153

The first statement holds true

198+153=351

The second statement holds true

1+3=4=5–1

The third statement holds true

The 3 digit number is 153