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

For more information on weighted averages, watch this video:

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let number of employees in Plutarch Enterprises be 100

No. of marketers(Mr)=70
No. of engineers(E)=20
No. of managers(Ma)=100-90=10

avg(Mr)=50k=sum/Mr
=>sum(Mr)=50k*70=350k

avg(E)=80k=sum/E
=>sum(E)=80k*20=160k

avg(Ma)=sum(Ma)/Ma
=>sum(Ma)=avg(Ma)*10

as Total average =80k
=>(sum(Ma)+sum(Mr)+sum(E))/Total=80k
=>avg(Ma)*10+160k+350K=80k*100=800k
=>avg(Ma)*10=290k
=>avg(Ma)=29K=$29000