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I have the following question in my homework.

In Company K, employees who work during the day have an average salary of 1500.00 and those who work at night, an average salary of 1100.00. The average salary of the company is to 1,400.00. What will be the percentage of employees who work during the day?

Which the easiest formula to return the result ?

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    If $p$ percent are day-workers, then $100-p$ percent are night-workers. It follows that the average salary is $\frac p{100}\cdot 1500 + \frac{100-p}{100}\cdot 1100$. By equating this with $1400$ you can solve for $p$.2012-09-18
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    Thanks, but unfortunately, I tryied without success, I know that the result is 75%, but I didn't get this result. Strange.2012-09-18

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Hint: If the fraction $p$ of the employees work during the day, $1-p$ work at night. The overall average is then $1500p+1100(1-p)$

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    Thanks the hint, but unfortunately, I tryied without success, I know that the result is 75%, but I didn't get this result. Strange.2012-09-18
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    @Lucas_Santos:yes, 75% is correct. The intuitive approach is that you need to go $\frac 14$ of the way from $1500$ to $1100$. You can plug $p=0.75$ into this to verify, then follow through your work to find where it stops working to find the error.2012-09-18
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    It really really helps. Thanks a lot.2012-09-18
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If you apply the formula $1500p+1100(1-p)=1400$ subtract $1400p$ from both sides gives

$100p +1100(1-p)=1400(1-p) $ dividing by $1-p$ gives

$100 p/(1-p)+1100 = 1400$ or

$100 p/(1-p)=300$ so

$p/(1-p)=3$ or $ p=3-3p $ implying $ 4p=3$ and $p=3/4$ or $75%$.