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
