3 men and 4 women can finish a piece of work in 12 days whereas 5 men and 4 women
can complete the same work in 9 days. Find the ratio of the amount of work done by a
man to the amount of work done by a woman.
Answers
Answer: the answer is stated below
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Step-by-step explanation:
3 men and 4 women can finish a piece of work in 12 days
3X+5Y=12----(1)
whereas 5 men and 4 women can complete the same work in 9 days.
5x+4y=9-----(2)
Find the ratio of the amount of work done by a man to the amount of work done by a woman.
find x:y
3X+5Y=12----(1)
3x=12-5y
x=(12-5y)/3----(3)
input equation 3 into equation 2
5x+4y=9-----(2)
but x=(12-5y)/3----(3)
therefore 5(12-5y)/3+4y=9
(60-25y)/3+4y=9
(60-13y)/3=9
multiply both sides by 3
60-25y+12y=27
collect like terms
60-27=25y-12y
33=13y
y=33/13
solve for the value of x
5x+4y=9-----(2)
y=33/13
5x+4(33/13)=9
5x+132/13=9
5x=9-132/13
5x=-15/13
x=-3/13 or 3/13 (i dont think days can be negative so i'm leaving two answeres)
to find the ratio of x to y
1) (33/13)/(-3/13)=-11
OR
2)(33/13)/(3/11)=11