Question 587964
LOT OF EXPLANATIONS (optional reading):
When you increase the price by 50%, you add to the previous price 50% of the previous price. That is 0.50 or {{{50/100}}} times the previous price.
So, if you started with a price P, after a 50% increase, the new price is
{{{P+(50/100)*P}}} or {{{P+0.5P=P(1+0.5)=1.5P}}}.
The idea, to calculate the new price after a certain percent increase or decrease is:
1) express that percent as a decimal (0.5 for 50%, 0.27 for 27%, 0.045 for 4.5%, and so on), using negative numbers for price decreases.
2) add 1 to that, to get your increase factor
3) multiply the old price times that factor
Example, a $60 dress, on sale at 12% off, costs
${{{60*(1-0.12)}}}=${{{60*0.88}}}=${{{52.80}}}
 
THE SOLUTION:
From an original price, P, an increase of 50% (0.5 as a decimal) brings the price up to
{{{P+0.5P=P(1+0.5)=1.5P}}}.
A new increase of x (expressed as a decimal) brings the price up to
{{{1.5P(1+x)}}}
If that equals 6 times the original price,
{{{1.5P(1+x)=6P}}}
We divide both sides by P, eliminating P, and then solve for x
{{{1.5P(1+x)=6P}}} --> {{{1.5(1+x)=6}}} --> {{{1.5+1.5x=6}}} --> {{{1.5+1.5x-1.5=6-1.5}}} --> {{{1.5x=4.5}}} --> {{{1.5x/1.5=4.5/1.5}}} --> {{{x=3}}}
A decimal of 3.00 mean an increase of 300%.
 
COMMENTS (more optional reading):
That is quite an increase.
If the original price was $200, the first 50% increase would have brought the price to $300.
Then the second (300%) increase would have quadrupled the previous $300 price to $1200, 6 times the original price.
That's hyperinflation. Ask anyone from Buenos Aires about it.
(There are other places that have had bad hyperinflation, but none that I visited).