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 Another Time And Work Problem (Posted on 2006-09-14)
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?

 See The Solution Submitted by K Sengupta Rating: 4.5000 (2 votes)

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 another way | Comment 3 of 4 |

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

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