Bunuel wrote:

4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?

(A) 24 days

(B) 32 days

(C) 36 days

(D) 40 days

(E) 42 days

Let's first

assign a "nice" value to the entire job.

We want a value that works well with 8 days and 10 days.

So, let's say

the job consists of making 80 widgetsLet M = the number of widgets 1 man can make in ONE day

Let W = the number of widgets 1 woman can make in ONE day

4 men and 6 women finish a job in 8 daysIn other words, 4 men and 6 women can make

80 widgets in 8 days

This means 4 men and 6 women can make 10 widgets in ONE day

So, we can write:

4M + 6W = 103 men and 7 women finish it in 10 daysIn other words, 3 men and 7 women can make

80 widgets in 10 days

This means 3 men and 7 women can make 8 widgets in ONE day

So, we can write:

3M + 7W = 8In how many days will 10 women working together finish it ?We already know that:

3M + 7W = 84M + 6W = 10Let's solve the system of equations for W

Take top equation and multiply both sides by 4 to get:

12M + 28W = 32Take bottom equation and multiply both sides by 3 to get:

12M + 18W = 30Subtract the bottom equation from the top equation to get: 10W = 2

Solve: W = 0.2

So, 1 woman can make 0.2 widgets in ONE day

This means 10 women can make 2 widgets in ONE day

So, 10 women can make

80 widgets in 40 days

Answer: D

Cheers

Brent

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