SOLUTION: A woman worked part-time certain number of days, receiving for her pay $ 1800. If she had received $ 10 per day less than she did, she would have had to work 3 days longer to ear

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A woman worked part-time certain number of days, receiving for her pay $ 1800. If she had received $ 10 per day less than she did, she would have had to work 3 days longer to ear      Log On


   

Question 1161652: A woman worked part-time certain number of days, receiving for her pay
$ 1800. If she had received $ 10 per day less than she did, she would
have had to work 3 days longer to earn the same sum. How many days
did she work?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
r, the woman's pay rate
highlight_green%281800%2Fr-1800%2F%28r-10%29=3%29
Simplify and solve for r.


If needed, according to rate x time = wages,
time in DAYS, rate in DOLLARS PER DAY
                     RATE         TIME(days)        WAGES

As Done              r            1800/r            1800

If lower rate       r-10          1800/(r-10)       1800

Difference                          3

Form the equation for the difference in number of days.

This is not yet the answer to the question. This helps find the pay rate. Expression 1800%2Fr will give how many days she did work.

-----------------A Different Way----------------------

The question asks for how many days she actually worked, d.
                       PayRate          Days          Wage
As Done               1800/d             d            1800
If                    1800/(d+3)         d+3          1800
Difference            10

The equation here is highlight_green%281800%2Fd-1800%2F%28d%2B3%29=10%29.
Solve this for d.

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.
A woman worked part-time certain number of days, receiving for her pay $1800.
If she had received $ 10 per day less than she did, she would have had to work 3 days longer
to earn the same sum. How many days did she work?
~~~~~~~~~~~~~~~~~~~~~


Regarding this problem,  one could  (and should)  expect that it has the solution in integer numbers of days.

I performed all calculations and found out that the problem  HAS  NO  solution in integer number of days.

Not only it has no solution in integer numbers of days - - - it has no solution in rational number of days, too.

Calculations leads to the  TRANSCENDENT  number of days,  which makes no any sense,  at all.


Therefore,  my conclusion is that this problem with its input data is a FAKE.


/\/\/\/\/\/\/\/

I deeply regret about my time,  which I spent for nothing,  working on this post.


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For the next generation of students who may read this post:


            Ignore writing by @josgarithmetic,  since it may lead you to  NOWHERE.