SOLUTION: State whether the following statement is true or​ false, and explain why. If the statement is​ false, state the true change. If the profits in your consulting business increas

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Question 1134655: State whether the following statement is true or​ false, and explain why. If the statement is​ false, state the true change.
If the profits in your consulting business increase by 77​% one year and decrease by 22​% the following​ year, your profits are up by 55​% over two years
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Let P be your base profit, the base value to compare with.


Then after one year the profit is P*(1+0.77), according to the condition, and after the second year the profit is  P*(1+0.77)*(1-0.22).


So, after two years your profit is P*1.77*0.78 = 1.3806P.


You compare it with the base profit P and see that the profit increased by 0.3386*P.


So, after two years the percentage of increasing your profit is   = 33.86%.     ANSWER


The statement in the post is FALSE, and I just explained why it is so.

Solved, explained and answered.

---------------

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    - Percentage word problems (Type 2 problems, Finding the Rate)
    - Percentage word problems (Type 3 problems, Finding the Base)
    - More complicated percentage problems
    - Problems on percentage that lead to unexpected results
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Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
profits increase by 77% one year and decrease by 22% the following year.

let's say your profits starts off as x.

if they increase by 77%, then the profits for the next year are equal to x + .77 * x which makes them equal to 1.77 * x.

if they then decrease by 22% the following year, then the profits for the following year would be 1.77 * x - .22 * 1.77 * x = 1.3806 * x.

your profits went from x to 1.3806 * x over the two year period.

that's an increase of .3806 * x which is equal to 38.06%.

here's how i think it works in dollars and cents.

assume your profits are 72 dollars for this year.

the next year they are increased by 77%.

the increase is therefore .77 * 72 = 55.44.

the profits next year are 72 + 55.44 = 127.44.

your profits the year after are decreased by 22%.

127.44 - .22 * 127.44 = 99.4032.

your profits over the two years are 99.4032 minus 72 = 27.4032.

that increase is 27.4032 / 72 = .3806 * 100 = 38.06%.

the 22% was taken off of next year's profit, not this year's profit.
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