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October 3rd, 2014, 09:35 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Arithmetic progression.
Two factories P and Q start to produce watches at the same time. a) Factory P produce x watches in the first month and increase constantly by y watches every subsequent month. It produces 155 watches in the 5th month and a total 910 watches in the first 7 months. Find the value of x and y. My answer x=55, y=25 b)Factory Q produces 100 watches in the first month and increase constantly by 15 watches every subsequent month. Find the month for both of the factories to produce the same quantity of watches. My answer is 5.5months. Is it correct? Last edited by skipjack; October 4th, 2014 at 02:17 AM. 
October 3rd, 2014, 11:00 AM  #2 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  It is.
Last edited by skipjack; October 4th, 2014 at 02:18 AM. 
October 3rd, 2014, 05:32 PM  #3 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
How about b?

October 4th, 2014, 02:14 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
I think in (b) they mean the month for when the total number of watches produced is the same, not just the number of watches in a single month. In that case the answer is 10. The total number of watches produced in 10 months is 1675 for each factory.

October 4th, 2014, 09:08 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,301 Thanks: 1023 
General case: 1st series : 1st term = a, difference = u 2nd series: 1st term = b, difference = v S = N[2a + u(N  1)] / 2 where: N = ABS[(2b  v  2a + u) / (v  u)] a = 55, u = 25, b = 100, v = 15 S = 1675 N = 10 ...as per Skiparoo 
October 4th, 2014, 02:48 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
You should have "" instead of "ABS", so that N = (2b  2a  (v  u))/(v  u) = 2(b  a)/(u  v) + 1.


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