If 65 percent of a certain firm’s employees are full-time and if there

Let x = the TOTAL number of employees

65 percent of a certain firm’s employees are full-time
This also means that 35 percent of the employees are part-time

So, 0.65x = the number of full-time employees
And 0.35x = the number of part-time employees

There are 5,100 more full-time employees than part-time employees
In other words: (the number of full-time employees) = (the number of part-time employees) + 5100
Substitute to get: 0.65x = (0.35x) + 5100
Subtract 0.35x from both sides of the equation to get: 0.3x = 5100
Divide both sides by 0.3 to get: x = 17,000

Answer: E

Cheers,
Brent

percent of a certain firm’s employees that are full-time = 65% of total employees

percent of a certain firm’s employees that are part-time = 100-65= 35% of total employees

(65-35)% of total employees = 5100

total employees = \(5100*\frac{100}{30 }\)= 17000

I think some word is missing in the red part?

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Fixed. Thank you.
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Let x be the total employees in the firm
--> \(\frac{65x}{100} = 5100 + \frac{35x}{100}\)

\(\frac{30x}{100}= 5100\)

\(x= \frac{5100*100}{30} = 17000\)

Answer (E)

let total employees = x
so
.65x=5100+.35x
x= 5100/.3
x= 17,000
OPTION E

It is given that 65% of x - 35% of x= 5100
30% of x =5100
x=5100*100/30
x=17000
E
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SOLUTION:
A NEW OG 2021 QUESTION

Its a question testing on basic application skills in percentage.

Let there be 100 employees.

Number of full time employees = 65

Number of part time employees = 100-65=35

The difference between full time and part time employees = 5100

=> 65-35 = 30 represents 5100

=>100(total employees) is represented by =(5100/30 )*100

=17000 (OPTION E)

Hope this helps
Devmitra Sen(Math)

Answer: Option E

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I have used to equations to find number of employees,

So let’s y be p/t employees and x total number of employees,

5100 + 2y = x,, y = ( x - 5100 ) / 2

.65x = 5100 + y

Solve for x will give you 1700 total number of employees.
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65% are full time so 35% are part time
Difference 30% is 5100
So 100% employees is 100*5100/30=17000
Option E is the answer
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I would build a 4-way ratio for this one. Full-time : Part-time : Total : Difference
Insert 65 and 100 into first and third columns, respectively, then reduce by the common factor of 5, so you get 13 and 20.
Now you can insert 7 into the second column, and finally you can insert 6 (13-7) into the last column.
Now we're ready for the actual number that they provided: 5,100 goes into the fourth column, and they want the third column.
Looking at our ratio, the third column is twenty-sixths, or ten-thirds as big as the fourth column.
What's ten-thirds of 5,100? Well, 1/3 of 51 is 17, so 1/3 of 5,100 is 1,700, so ten-thirds of 5,100 is 17,000.
Big takeaway for this category of question: don't rush to use the actual number that they provide. First, take your time to set up all the ratio columns that would be useful, and insert your inferences in the world of ratios.
Only then, as a final step, bring in the information from the world of actual numbers.
Reason: working with a ratio (a simplified model of reality) is a lot easier than working with the actual numbers.

Total employees is PT plus FT. So if I write equation FT = 0.65 (FT+PT), i get answer 11050. Other equation being FT = 5100+PT. Why is the first equation incorrect? Please explain.

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65% of full time employees
so 35% part time

65x/100-35x/100=5100
x=17000

The answer is E after a proper equation is formed

Posted from my mobile device

You have calculated FT (=11050). Now add PT(=5950) to FT to get 17000