A recycling facility is staffed by eight floor workers

[shreerajp99]

A recycling facility is staffed by eight floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid q times as much as a floor worker. If the manager’s wages account for 1/7 of all wages paid at the facility, what is the value of q?

A 4/3
B 9/7
C 5/4
D 11/9
E 8/7

I tried to use numbers here and set up the equation as follows:
say each worker is paid $10,so 8 workers will get $80.Since a manager's pay(x) is 1/7(total pay) so then i set the equation as:

x=1/7(80+x)

x=80/7 + x/7

x=13.33

Now since a manager is paid q times a worker,the equation would be:
8q=13.33
q=1.66 but then this ans isnt there in any of the options.

Can u plz tell me where im going wrong?

Thanks,
Shreeraj

[sieb2004]

8x = 6/7 => x = 6/(7*8) = 3/28
qx = 1/7 => q = (1*28)/(7*3) = 4/3
A (4/3).
What is the OA?

[jnelson0612]

Sheeraj, what is the original source of this question? For some reason I am thinking that it is from the OG 13.

When I did this question I just chose a number for the entire salary. I wanted something that is both divisible by 7 AND that yields a result divisible by 8 once the 1/7 is deducted.

I started considering multiples of 7. 28 is the first one that fit the bill: take out 1/7 for the manager pay, $4, and that leaves $24 for 8 workers. That means that they each get $3. Thus, the manager gets 4/3 as much as each worker.