SOLUTION: An original number is increased by k%, and then the result is decreased by w%. The final result is 85% of the original number. If k is a positive integer less than 173 and if w is

Question 1017725: An original number is increased by k%, and then the result is decreased by w%. The final result is 85% of the original number. If k is a positive integer less than 173 and if w is a positive integer, find the sum of all possible distinct values of k.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= the original number
= 85% of the original number
= the original number increased by .
Increasing a number by is multiplying it by .
Similarly, decreasing a number by is multiplying it by :
.
So,
= the original number first increased by , and then decreased by .
Our equation is

Now we need pairs of factors of
There should be factors, which come in pairs:
,
,
,
,
,
,
,
,
,
,
, and
.
Since , .
The only factors that could be are , , and .
--->---> , or
--->---> , or
--->---> .
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