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?

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

9 times the first equation minus 2 times the second gives:

21m + 28b = 2380

Dividing by 7 gives:

3 m + 4 b = 340 $/day

2380/340 = 7 days (obviously, since we divided the first 2380 by 7).

Why 9 and -2?

FOR i = -40 TO 40
FOR j = -40 TO 40
  m = 12 * i + 5 * j
  b = 13 * i + 6 * j
  IF 4 * m = 3 * b THEN
   PRINT i, j
   PRINT m, b: PRINT
  END IF
NEXT
NEXT

prints, in part:

-2             9
 21            28

Posted by Charlie on 2006-09-14 14:02:05