anonymous
  • anonymous
help
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
after \(N\) weeks, Eduardo spends \(7500+300 \cdot N\)
Michele_Laino
  • Michele_Laino
and after \(N \) weeks he earns \(850 \cdot N\), so Eduardo will have a profit if the subsequent condition holds: \[850 \cdot N \geqslant 7500 + 300 \cdot N\] namely earnings are greater or equal than expenses

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Michele_Laino
  • Michele_Laino
please you have to solve that inequality
anonymous
  • anonymous
Idk how
Michele_Laino
  • Michele_Laino
If I subtract \(300N\) from both sides I get this: \[850N - 300N \geqslant 7500 + 300N - 300N\] please simplify
anonymous
  • anonymous
would that be 850-300 for the first part?
Michele_Laino
  • Michele_Laino
yes!
anonymous
  • anonymous
Ok! 550 right?
Michele_Laino
  • Michele_Laino
correct! and what is +350-350=...?
Michele_Laino
  • Michele_Laino
oops.. what is +300-300=...?
anonymous
  • anonymous
0
anonymous
  • anonymous
I think
Michele_Laino
  • Michele_Laino
ok! so we get this inequality: \[550N > 7500\]
anonymous
  • anonymous
ok
Michele_Laino
  • Michele_Laino
I wrote \(>\) because it is better than \(\geqslant \)
anonymous
  • anonymous
ok
anonymous
  • anonymous
so what would I have to do next?
Michele_Laino
  • Michele_Laino
now, we have to divide both side by 550, so we have: \[\frac{{550N}}{{550}} > \frac{{7500}}{{550}}\] please simplify again
anonymous
  • anonymous
How would I simplify those
Michele_Laino
  • Michele_Laino
what is 7500/550=...?
anonymous
  • anonymous
13.636
Michele_Laino
  • Michele_Laino
and what is 550/550=...?
anonymous
  • anonymous
1
Michele_Laino
  • Michele_Laino
ok so we get this: \(1 \cdot N > 13.6363...\)
Michele_Laino
  • Michele_Laino
since the number of week has to be a whole number we can choose N=14
anonymous
  • anonymous
so it would be 14 weeks?
Michele_Laino
  • Michele_Laino
yes!
anonymous
  • anonymous
Oh ok thanks
Michele_Laino
  • Michele_Laino
:)
anonymous
  • anonymous
I have one more
anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
If I call with P the age of Pat and with R the age of Ron, then from the text of your problem, I can write this: \[\begin{gathered} 2P + 5 = R \hfill \\ P + R < 35 \hfill \\ \end{gathered} \]
anonymous
  • anonymous
ok
anonymous
  • anonymous
I'm sorry my internet went down for a few minutes

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