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4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini

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4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 26 Nov 2018, 06:28
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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

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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 26 Nov 2018, 07:07
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1
In 1 day,
4m+6w = 1/8 (of the work)
3m+7w = 1/10 (of the work)

multiply:
12m+28w = 4/10
12m+18w = 3/8

subtract:
10w = 2/80
10w = 1/40 (of the work)

So 10 women need 40 days to complete a work
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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 26 Nov 2018, 07:09
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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 widgets

Let 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 days
In 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 = 10

3 men and 7 women finish it in 10 days
In 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 = 8


In how many days will 10 women working together finish it ?
We already know that:
3M + 7W = 8
4M + 6W = 10
Let's solve the system of equations for W

Take top equation and multiply both sides by 4 to get: 12M + 28W = 32
Take bottom equation and multiply both sides by 3 to get: 12M + 18W = 30

Subtract 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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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 26 Nov 2018, 07:43
Mahmoudfawzy83 wrote:
In 1 day,
4m+6w = 1/8 (of the work)
3m+7w = 1/10 (of the work)

multiply:
12m+28w = 4/10
12m+18w = 3/8

subtract:
10w = 2/80
10w = 1/40 (of the work)

So 10 women need 40 days to complete a work

I like the approach you solved

we just need to simplify the 2 eqns by multiplying with common term -3 and 4 respectively
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4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 26 Nov 2018, 08:36
GMATPrepNow wrote:
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 widgets

Let 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 days
In 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 = 10

3 men and 7 women finish it in 10 days
In 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 = 8


In how many days will 10 women working together finish it ?
We already know that:
3M + 7W = 8
4M + 6W = 10
Let's solve the system of equations for W

Take top equation and multiply both sides by 4 to get: 12M + 28W = 32
Take bottom equation and multiply both sides by 3 to get: 12M + 18W = 30

Subtract 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


hello Brent: nice explanation :) 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 ?
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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 26 Nov 2018, 16:19
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



4M+6w=1/8
3M+7W=1/10

solve for M &W
we will get 12M+18W=3/8 &
12M+28W=4/10

10W=1/40

Option D
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4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 27 Nov 2018, 00:00
what is the logic when we subtract one equation from another ?
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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini  [#permalink]

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New post 27 Nov 2018, 00:22
dave13 wrote:
what is the logic when we subtract one equation from another ?


IN an equality equations, the '=' sign says that both sides have the same value,

so in: 12m+28w = 4/10,

let subtract both sides with (3/8):

12m + 28w - (3/8) = 4/10 - 3/8

from the other equation, we know that 12m+18w = 3/8
so we can replace (3/8) with (12m+18w) at one side of the first equation as follows:

12m + 28w - (12m+18w) = 4/10 - 3/8
12m + 28w - 12m -18w = 4/10 - 3/8
10w = 1/40

I hope I got your question right.
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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini &nbs [#permalink] 27 Nov 2018, 00:22
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