## anonymous one year ago 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work? ans is 8 or 12.5?

1. vanessaperezxo

I think the answer would be 12.5

2. vanessaperezxo

because for it to be done in 8 day you need 3 men and 2 boys.. so if you have 2 men 1 boy it's going to take a few extra days. Do you get it? @yashiii

3. vanessaperezxo

@yashiii you there?

4. anonymous

yup....i think i solved it incorrectly .my ans was 8 ..hehhe

5. anonymous

@welshfella

6. vanessaperezxo

Oh ok, i have to go. Good luck solving the problem. sorry

7. anonymous

bye :) @vanessaperezxo

8. Michele_Laino

If I call with x the working rate of a man, and with y the working rate of a boy, then I can write this algebraic system: $\Large \left\{ \begin{gathered} 2x + 3y = \frac{W}{{10}} \hfill \\ 3x + 2y = \frac{W}{8} \hfill \\ \end{gathered} \right.$ where W is the work to be done

9. phi

2 men and 3 boys can do a piece of work in 10 days 2 men and 1 boy will take longer (less help) so if it's a choice between 8.5 and 12.5, pick 12.5

10. anonymous

a similar approach is to solve $10(2x+3y)=1\\ 8(3x+2y)=1$ which is not that elegant but works

11. anonymous

but as @phi said, common sense tells you it is longer than 8 it is in fact 12.5

12. anonymous

actually i want correct ans...those ans options were imaginary .:(

13. anonymous

how did you guess at the correct answer of 12.5?

14. anonymous

now i got ans 13.5 , so any one can pls tell me the accurate ans

15. anonymous

12.5 is correct

16. anonymous

@satellite73 , on any website someone solved it ,but other people were saying that ans is wrong. so m confused

17. anonymous

we can do it step by step, although i guess there probably a better method than i used

18. anonymous

put men's rate as x, boys at y the first two statements translates as $10(2x+3y)=1\\ 8(3x+2y)=1$

19. anonymous

solving this for x and y gives $x=\frac{7}{200},y=\frac{1}{100}$

20. anonymous

@Michele_Laino , you have ne idea

21. anonymous

acha..okay..got it now :)

22. anonymous

oops i means solve $T\left(\frac{14}{200}+\frac{1}{100}\right)=1$

23. anonymous

and that gives $$T=12.5$$

24. anonymous

okay

25. Michele_Laino

I agree with @satellite73 we have to solve that system above, so we can find the requested time

26. anonymous

like i said, there may be a snappier way to do it, i don't know it

27. anonymous

@satellite73 , @Michele_Laino , thankyou so much both of you :)

28. Michele_Laino

:)