|
Question 723064: Please solve this word problem ; The middle digit of a three digit number is zero. The number is 34 times the sum of its digit. The new number obtained by interchanging the digit in the unit's and the hundered's place is more than the original number by 396. Find the original number.
Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The middle digit of a three digit number is zero. The number is 34 times the sum of its digit. The new number obtained by interchanging the digit in the unit's and the hundered's place is more than the original number by 396. Find the original number.
***
let u=units digit
let t=tens digit=0
let h=hundreds digit
..
100h+0+u=34(h+0+u)
..
100u+h-100h-u=396
99u-99h=396
99(u-h)=396
u-h=396/99=4
u=4+h
..
100h+u=34(h+u)
plug in (4+h) for u
100h+4+h=34(h+4+h)
101h+4=68h+136
33h=132
h=4
u=4+h=8
original number:100h+u=400+8= 408
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! The middle digit of a three digit number is zero.
Meaning, three digit number is  , where h is the digit in the hundreds place and u is the digit in the ones place.
The number is 34 times the sum of its digit.
Meaning,  .
The new number obtained by interchanging the digit in the unit's and the hundered's place is more than the original number by 396.
Meaning,  .
The goal is to find what is h and u, or what is . I'd try to use the "34" equation to make a substitution in the inequality, and then solve the inequality.
proceeding with the "34" equation,  ,
2h=u, or  .
Do that substitution.
 , 67h>132, h>132/67, 
RESULTS:
The hundreds place COULD be 2. Will this work? If so, the u=4. (YES).
Hundreds place could be 3, and then u=6.
Hundreds place could be 4, and then u=8.
THOSE ALL WORK. 204, 306, 408.
|
|
|
| |
