In a certain office, the ratio of men to women is 3/4. If 10 men were

m/w= 3/4
m+10/w=7/6

solve for M =18 and w =24 m+ w= 42 option D

Solution

Given:

• The ratio of men to women = \(\frac{3}{4}\)
• If 10 men were added, then ratio of men to women would be \(\frac{7}{6}\)

To find:

• The total number of men and women in the office currently

Approach and Working:

• \(\frac{M}{W} = \frac{3}{4}\)
• \(\frac{(M + 10)}{W} = \frac{7}{6}\)

o \(\frac{M}{W} + \frac{10}{W} = \frac{7}{6}\)
o \(\frac{10}{W} = \frac{7}{6} – \frac{3}{4} = \frac{(14 – 9)}{12} = \frac{5}{12}\)

• Thus, W = \(10 * \frac{12}{5} = 24\)
• Implies, M = \(3 * \frac{24}{4} = 18\)

Therefore, M + W = 18 + 24 = 42

Hence, the correct answer is Option D

Answer: D

In a certain office, the ratio of men to women is 3/4.
This tells us that, out of EVERY 7 people in the office, 3 are men and 4 are women.
It also tells us that the TOTAL number of men and women currently in the office is divisible by 7
When we check the answer choices, we see that A, B and E are NOT divisible by 7
So, we can ELIMINATE A, B and E

Now that we have just 2 answer choices remaining, we can just TEST the 2 remaining answer choices...

If 10 men were added to the office, the ratio of men to women would be 7/6.
This tells us that the NEW number of men and women in the office is divisible by 13 [since 7+6 = 13]
Let's check the REMAINING answer choices.

C) 28
When we add 10 to 28, we get 38
Since 38 is NOT divisible by 13, we can ELIMINATE C

D) 42
When we add 10 to 42, we get 52, which IS divisible by 13

Answer: D

Cheers,
Brent

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

A simple one. This is how I solved:

Posted from my mobile device

We can let 3x = the number of men and 4x = the number of women currently in the office. Thus we have:

(3x + 10)/4x = 7/6

6(3x + 10) = 7(4x)

18x + 60 = 28x

60 = 10x

6 = x

So there are 18 men and 24 women, or a total of 42 men and women in the office.

Answer: D

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