## In Plutarch Enterprises, $$70\%$$ of the employees are marketers, $$20\%$$ are engineers, and the rest are managers.

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### In Plutarch Enterprises, $$70\%$$ of the employees are marketers, $$20\%$$ are engineers, and the rest are managers.

by VJesus12 » Thu Sep 16, 2021 11:16 am

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## Global Stats

In Plutarch Enterprises, $$70\%$$ of the employees are marketers, $$20\%$$ are engineers, and the rest are managers. Marketers make an average salary of $$\50,000$$ a year, and engineers make an average of $$\80,000.$$ What is the average salary for managers if the average for all employees is also $$\80,000?$$

A. $$\80,000$$
B. $$\130,000$$
C. $$\240,000$$
D. $$\290,000$$
E. $$\320,000$$

Source: Magoosh

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### Re: In Plutarch Enterprises, $$70\%$$ of the employees are marketers, $$20\%$$ are engineers, and the rest are managers.

by [email protected] » Thu Sep 16, 2021 3:22 pm
VJesus12 wrote:
Thu Sep 16, 2021 11:16 am
In Plutarch Enterprises, $$70\%$$ of the employees are marketers, $$20\%$$ are engineers, and the rest are managers. Marketers make an average salary of $$\50,000$$ a year, and engineers make an average of $$\80,000.$$ What is the average salary for managers if the average for all employees is also $$\80,000?$$

A. $$\80,000$$
B. $$\130,000$$
C. $$\240,000$$
D. $$\290,000$$
E. $$\320,000$$

Source: Magoosh
We can solve this using weighted averages

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + . . .

We're told that:
The marketers (with an average annual salary of $50,000) comprise 7/10 of the group The engineers (with an average annual salary of$80,000) comprise 2/10 of the group
The managers (with an average annual salary of $x) comprise 1/10 of the group The average salary of all groups COMBINED = 80,000 Applying the formula we get: 80,000 = (7/10)($50,000) + (2/10)(\$80,000) + (1/10)(x)
Simplify: 80,000 = 35,000 + 16,000 + 0.1x
Simplify: 80,000 = 51,000 + 0.1x
We get: 29,000 = 0.1x
Solve: x = 290,000