At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age

[M M7MBA]

At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

[Brent@GMATPrepNow]

At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

This is a nice weighted averages question.

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

So: average age of COMBINED workers = (proportion of project managers)(average age of project managers) + (proportion of engineers)(average age of engineers)

We have a total of 24 workers (14 project managers + 10 engineers = 24 workers)
So, the proportion of project managers = 14/24 = 7/12
The proportion of engineers = 10/24 = 5/12
Let E = average age of engineers

Now, plug everything into the formula to get:
31 = (7/12)(36) + (5/12)(E)
Simplify: 31 = 21 + 5E/12
Subtract 21 from both sides: 10 = 5E/12
Multiply both sides by 12 to get: 120 = 5E
Solve: E = 24

Answer: A

Cheers,
Brent

[Scott@TargetTestPrep]

At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30

[spoiler]OA=A[/spoiler]

Solution:

Letting n = the average age of the engineers, we can create the equation:

(14 x 36 + 10n)/24 = 31

504 + 10n = 744

10n = 240

n = 24

Answer: A