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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?

Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Solution: (Hide)

7 days.

EXPLANATION:

Let the daily earnings of each man and each of the boys be denoted respectively by M and B.

Then, by the problem:

12M + 13B = 3720/3 = 1240
5M + 6B = 2700/5 = 540ЕЕ..(#)

Solving, we obtain (M, B) = (60, 40) and accordingly:
Daily earnings of 3 Men and 4 Boys is 60*3 + 40*4 = $340; so that:
3 Men and 4 Boys will earn $2380 in 2380/340 = 7 days.

For the Bonus Question:

Let p(12M + 13B) + q(5M+6B) = 3M+4B
Or, (12p + 3q, 13p+6q) = (3,4)
Solving, we obtain:
(p, q) = (-2/7, 9/7); and so, in terms of (#), we obtain:

7(3M + 4B)
= (-2)*(12M+13B) + (9)*(5M + 6B)
= -2* 1240 + 9*540
= 2380

Hence, the required time for 3 men and 4 Boys to earn $ 2380 is 7 days.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Second way	Old Original Oskar!	2006-09-14 15:30:26
another way	Charlie	2006-09-14 14:02:05
bonus question	Stefan Petszaft	2006-09-14 13:54:27
solution	John	2006-09-14 13:36:07

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