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. \(\$320,000\)

Answer: D

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

Answer: D