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Question 996439: The sum of a three digit number is 14. The number is 14 larger than twenty times the tens digit. The sum of the tens digit and the unit digit is 12 larger than the hundreds digit. Find the number.
Answer by phillywily(18)   (Show Source):
You can put this solution on YOUR website! Let x be the original number, a be the hundreds' digit, b be the tenths' and c be the ones.
Form 4 equations from the question.
Equation 1:100a+10b+c=x
Equation 2:a+b+c=14
Equation 3:c+b=a+12
Equation 4:14+20b=x
1. Find the similarity of these 4 equations. You could realize how equation 2 and 3 is similar
(a+b+c=14)
↓
(c+b=14-a)
c+b=a+12
Both of them are equivalent to c+b, which means 14-a=a+12. Here you got a linear equation.
2. Solve for a.
14-a=a+12
-a-a=12-14
-2a=-2
a=1
3. Substitute a=1 to equation 3.
c+b=12+a
c+b=12+1
c+b=13
4. Choose either to solve b or c first. I personally choose to solve for c. So I can conclude that,
b=13-c
5. Substitute b=13-c into equation 1 and 4. Now you got another similarity since both equations equal x.
x=100+10(13-c)+c
x= 14+20(13-c)
6. Now you can find c.
100+10(13-c)+c=14+20(13-c)
100+130-10c+c=14+260-20c
230-9c=274-20c
20c-9c=274-230
11c=44
c=4
7. Now you can find b.
a+b+c=14
5+b=14
b=9
8. Now you can see
a=1
b=9
c=4
9. So now you get the final answer.
x=194
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