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# algebra problem

## Tags: Mathematik     RASTA 00:33 Uhr, 29.07.2022

Tag!
Concert organizers set the admission price at 25 dollars. After the concert took place they note that they have suffered a loss of 4250 dollars. If the entry price had been 30 dollars, the deficit would have been only 1500 dollars. How many paying spectators were there?

Please, I need a hint to start me off on this problem.
to see the concert, concert goers have to pay 25 dollars.
loss of money for the organizers they came out 4250 short of hat they had invested in the concert
if every goer had paid 30 dollars they would only have lost 1500 dollars.

Welchen Tipp würden Sie mir für den Anfang geben?

Danke im Voraus.  pivot 02:38 Uhr, 29.07.2022

Hello,

first of all I woud set up the profit/loss finction $P\phantom{\rule{0.12em}{0ex}}\left(x\phantom{\rule{0.12em}{0ex}}\right)$.

$P\phantom{\rule{0.12em}{0ex}}\left(x\phantom{\rule{0.12em}{0ex}}\right)=p\phantom{\rule{0.12em}{0ex}}\cdot x\phantom{\rule{0.12em}{0ex}}-C\phantom{\rule{0.12em}{0ex}}$

X ist the number of sold tickets. p is the ticket price. $p\phantom{\rule{0.12em}{0ex}}\cdot x\phantom{\rule{0.12em}{0ex}}$ is therefore revenue.
And $C\phantom{\rule{0.12em}{0ex}}$ are the costs, which are fix (constant).

Now we insert the given values.

$25\cdot x\phantom{\rule{0.12em}{0ex}}-C\phantom{\rule{0.12em}{0ex}}=-4250$
$30\cdot x\phantom{\rule{0.12em}{0ex}}-C\phantom{\rule{0.12em}{0ex}}=-1500$

A negtive profit is a loss. It remains to solve this little equation system. I recommend to subtract one equation from the other. Then C disappears. Take care of the signs.

greetings,
pivot  supporter 06:25 Uhr, 29.07.2022

alternative:

$25x\phantom{\rule{0.12em}{0ex}}-C\phantom{\rule{0.12em}{0ex}}=-4250\to C\phantom{\rule{0.12em}{0ex}}=25x\phantom{\rule{0.12em}{0ex}}+4250$

$30x\phantom{\rule{0.12em}{0ex}}-\left(25x\phantom{\rule{0.12em}{0ex}}+4250\right)=-1500$

$x\phantom{\rule{0.12em}{0ex}}=...$.

Put the result into one of the two initial equations to get C.  RASTA 15:44 Uhr, 29.07.2022

Thank you very much, pivot for your help.
here I show my work for the system of equations you left me to solvve

$25x\phantom{\rule{0.12em}{0ex}}-C\phantom{\rule{0.12em}{0ex}}=-4250$

$30x\phantom{\rule{0.12em}{0ex}}-C\phantom{\rule{0.12em}{0ex}}=-1500$

As you advise I subtracted both equations.

$-5x\phantom{\rule{0.12em}{0ex}}=-2750$

$-5\frac{x\phantom{\rule{0.12em}{0ex}}}{-5}=-\frac{2750}{-5}$

$x\phantom{\rule{0.12em}{0ex}}=550$

so the answer is there were $550$ paying spectators present.  supporter 16:05 Uhr, 29.07.2022

You result is correct. :-)  RASTA 16:06 Uhr, 29.07.2022

Vielen Dank!!