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
what if i didnt assign value to the total job done, and in the end get 0.2, how should i figure ourt correct answer ?