If 12 men and 13 boys can earn $3,720 in 3 days, while 5 men and 6 boys can earn $2,700 dollars in 5 days, how long will it take for 3 men and 4 boys to earn $2,380?

Bonus Question: Can you solve this without working out how much does a man or a boy earn per day?

we have for 1 day:

m = men
b = boys
d = days

12*m + 13*b = 3720/3
5*m + 6*b = 2700/5

so 7*m + 7*b = 3720/3-2700/5 = 700

-> m+b = 100

taking the second equation we find that:

d*(3*m + 4*b) = d*(5*m+6*b - 200)

so in five days

3 men and 4 boys get 2700$-1000$ = 1700$

we then do  2380/(1700/5) = 7

so the answer is 7 days
 

Posted by John on 2006-09-14 13:36:07