In a certain store, the ratio of part-time workers to full-time workers is 2 to 5

BTGModeratorVI wrote: ↑

Fri Feb 28, 2020 9:56 am

In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11
(B) 12
(C) 21
(D) 28
(E) 35

Answer: D
Source: Veritas Prep

We can use two variables to solve this (although 1 variable is typically faster)

The ratio of part-time workers to full-time workers is 2 to 5\
Let P = number of Part-time workers
Let F = number of Full-time workers
We can write: P/F = 2/5
Cross multiply to get: 5P = 2F


If 4 part-time workers were hired, then the ratio would be 3 to 5.
This would mean there are no P+4 part-time workers
Also, there are still F full-time workers
We can write: (P+4)/F = 3/5
Cross multiply to get: 5(P + 4) = 3F
Expand to get: 5P + 20 = 3F
Replace 5P with 2F to get: 2F + 20 = 3F
Solve to get F = 20
So, there are presently 20 full-time employees

How many workers does the store have?
Since F = 20, we can use the equation 5P = 2F to help find the value of P
Replace F with 20 to get: 5P = 2(20)
Simplify: 5P = 40
Solve to get: P = 8

TOTAL number of workers = F + P = 20 + 8 = 28

Answer: D

Cheers,
Brent