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October 3rd, 2014, 09:35 AM   #1
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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.
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October 3rd, 2014, 11:00 AM   #2
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Quote:
Originally Posted by jiasyuen View Post

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

Is it correct?
It is.

Last edited by skipjack; October 4th, 2014 at 02:18 AM.
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October 3rd, 2014, 05:32 PM   #3
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How about b?
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October 4th, 2014, 02:14 AM   #4
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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.
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October 4th, 2014, 09:08 AM   #5
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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
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October 4th, 2014, 02:48 PM   #6
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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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