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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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    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

2 Answers 2

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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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    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 $75%$.