SOLUTION: 4 men and 10 women were put on a work. They completed 1/3 of the work in 4 days. After this 2 men and 2 women were increased. They completed 2/9 more of the work in 2 days. If th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 4 men and 10 women were put on a work. They completed 1/3 of the work in 4 days. After this 2 men and 2 women were increased. They completed 2/9 more of the work in 2 days. If th      Log On


   

Question 884284: 4 men and 10 women were put on a work. They completed 1/3 of the work in
4 days. After this 2 men and 2 women were increased. They completed 2/9
more of the work in 2 days. If the remaining work is to be completed in 3
days, then how many more women must be increased ?
The answer is 8. I need the solution.
Thank You.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
RT=J Basic Equation, rate, time, job.

Let m = rate for 1 man
Let w = rate for 1 woman
Each work session is build on a term RT but specifically these are in parts of 1/3, 2/9, and the remaining part of the job to make one whole job.

%284m%2A4%2B10w%2A4%29=1%2F3
-
6m%2A2%2B12w%2A2=2%2F9
-
How many more men, working 3 more day?
Let q = the additional number of men
%286%2Bq%29m%2A3%2B12w%2A3=1-%281%2F3%2B2%2F9%29
-
BE SURE YOU UNDERSTAND EACH OF THOSE THREE EQUATIONS BEFORE CONTINUING. The first is accounting for the amount of work in the first four days; the second is accounting for the work in the next two day; the last is accounting for the last portion of the work using unknown q increased men in that last three days of work.

Observe how those THREE equations use THREE unknown variables. This appears to NOT be a linear system. This should not be a major difficulty because the first two equations form a system of TWO equations in TWO unknowns, m and w, to be found first.


SIMPLIFY THE WHOLE SYSTEM:
16m%2B40w=1%2F3
highlight_green%2848m%2B120w=1%29
-
12m%2B24w=2%2F9
6m%2B12w=1%2F9
highlight_green%2854m%2B108w=1%29
-
%286%2Bq%29m%2A3%2B12w%2A3=1-%281%2F3%2B2%2F9%29
18m%2B3mq%2B36w=9%2F9-%283%2F9%2B2%2F9%29
18m%2B3mq%2B36w=%284%29%2F9
and because we really will later want to solve for q,
3mq=4%2F9-18m-36w
q=%284%2F9-18m-36w%29%2F%283m%29
highlight_green%28q=4%2F27-6m-12w%29
The simplified equations are shown outlined in highlight_green%28GREEN%29.

SOLVE THE SYSTEM:
First solve for m and w in the first two equations as a separate subsystem. I suggest substitution method because the coefficients are not very convenient for using elimination method.
USE the values for m and w found, and compute the value for q.

The rest of that "SOLVE THE SYSTEM" work is undone here but you should (need ) to do it.