BTGModeratorVI wrote: ↑Mon Jun 22, 2020 6:20 am
In a certain office, the ratio of men to women is 3/4. If 10 men were added to the office, the ratio of men to women would be 7/6. How many men and women total are currently in the office?
A. 18
B. 24
C. 28
D. 42
E. 52
Answer:
D
Source: Princeton Review
Another approach:
Let M = number of men CURRENTLY in the office
Let W = number of women CURRENTLY in the office
In a certain office, the ratio of men to women is CURRENTLY 3/4.
We can write: M/W = 3/4
Cross multiply to get: 4M = 3W
Rewrite as:
4M - 3W = 0
If 10 men were added to the office, the ratio of men to women would be 7/6
So, M+10 = number of men HYPOTHETICALLY in the office
We can write: (M + 10)/W = 7/6
Cross multiply to get: 6(M + 10) = 7W
Expand left side to get: 6M + 60 = 7W
Rewrite as:
6M - 7W = -60
How many men and women total are CURRENTLY in the office?
We have the following system of equations:
4M - 3W = 0
6M - 7W = -60
Take the TOP equation and multiply both sides by 3.
Take the BOTTOM equation and multiply both sides by 2.
We get:
12M - 9W = 0
12M - 14W = -120
Subtract bottom equation from top equation to get: 5W = 120
Solve: W = 120/5 = 24
So, there are CURRENTLY 24 women
To find the value of M, plug W = 24 into any equation.
Take 4M = 3W and replace W with 24 to get: 4M = 3(24)
Solve: M = 18
So, there are CURRENTLY 18 men
The TOTAL number of people CURRENTLY in the office = 24 + 18 = 42
Answer: D
Cheers,
Brent
