SOLUTION: The value of the ones digit of a three-digit number is the sum of the hundreds and and tens digit. The difference between the hundreds and tens digit is 6. If the order of the digi

Algebra ->  Finance -> SOLUTION: The value of the ones digit of a three-digit number is the sum of the hundreds and and tens digit. The difference between the hundreds and tens digit is 6. If the order of the digi      Log On


   

Question 1188077: The value of the ones digit of a three-digit number is the sum of the hundreds and and tens digit. The difference between the hundreds and tens digit is 6. If the order of the digits is reversed, the resulting number is 99 more than the original number. Find the original number.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The number, 100h%2B10t%2Bu

system%28u=h%2Bt%2Cabs%28h-t%29=6%2C100u%2B10t%2Bh-%28100h%2B10t%2Bu%29=99%29

99u-99h=99
u-h=1

Revising the system
system%28u=h%2Bt%2Cabs%28h-t%29=6%2Cu-h=1%29

system%28u-h=t%2Cabs%28h-t%29%2Cu-h=1%29
Looking at eq. 1 and eq. 3 here, value for t should be 1;
highlight_green%28t=1%29

abs%28h-t%29=6
Either h-t=6
Or
h-t=-6
--
If t=1, then h-1=6
h=7
or
h=-6%2B1----------this is no good.
-
highlight_green%28h=7%29

Finding the ones digit
u=h%2Bt
u=7%2B1
highlight_green%28u=8%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution from the other tutor is a perfectly good formal algebraic solution; you should understand it.

For a faster path to the answer (if formal algebra is not required), use the fact that when a 3-digit number is reversed, the new number is 99 times the difference between the hundreds and units digit.

In this problem, reversing the digits increases the value of the number by 99; that means the hundreds digit is one LESS than the units digit.

That, combined with the knowledge that the ones digit is the sum of the hundreds and tens digit, means the tens digit is 1.

Then, since the difference between the hundreds and tens digits is 6, the hundreds digit is 7; and since the hundreds digit is one less than the units digit makes the units digit 8.

ANSWER: The number is 718