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Arithmetic progressions

A woman started a business with a workforce of 50 people. Every two weeks the number of people in the workforce increased by 3 people.

a) How many people were there in the workforce after 26 weeks?

2 weeks = 3 more people
26 weeks = 13 additions so, 13 X 3 = 39 + 50 = 89. this was correct.

b) Each member of the workforce earned $600 per week. What was the total wage will for this 26 weeks?

My working:
$600 per person per week
first 2 weeks = 2 (600 X 50) = $60 000
so a is 60 000
Every 2 weeks, which can be said to be one addition as it is constant, 2 (3 X 600) = $3600 is added
So d is 3600
n is (26/2 + 1) = 14
Sum = n/2 (2a + (n-1)d)
= 7 (120 000 + (13)3600)
= $1 167 600
This is wrong. The correct answer is $1 341 600. What am I doing wrong???
Reply 1
Original post by Jmun
A woman started a business with a workforce of 50 people. Every two weeks the number of people in the workforce increased by 3 people.

a) How many people were there in the workforce after 26 weeks?

2 weeks = 3 more people
26 weeks = 13 additions so, 13 X 3 = 39 + 50 = 89. this was correct.

b) Each member of the workforce earned $600 per week. What was the total wage will for this 26 weeks?

My working:
$600 per person per week
first 2 weeks = 2 (600 X 50) = $60 000
so a is 60 000
Every 2 weeks, which can be said to be one addition as it is constant, 2 (3 X 600) = $3600 is added
So d is 3600
n is (26/2 + 1) = 14
Sum = n/2 (2a + (n-1)d)
= 7 (120 000 + (13)3600)
= $1 167 600
This is wrong. The correct answer is $1 341 600. What am I doing wrong???


(30000+30000)+(31800+31800)+(33600+33600)+(35400+35400)+...


n=13, a = 2 x 50 x 600, d = 2 x 3 x 600
(edited 8 years ago)
Reply 2
Original post by TeeEm
(30000+30000)+(31800+31800)+(33600+33600)+(35400+35400)+...


n=13, a = 2 x 50 x 600, d = 2 x 3 x 600


n is 14 because you include the first term. Sorry but i still dont get what it did wrong... i did what you said here.
Reply 3
Original post by Jmun
n is 14 because you include the first term. Sorry but i still dont get what it did wrong... i did what you said here.


I suggest you write all the 14 terms out without (...)
Original post by Jmun
n is 14 because you include the first term. Sorry but i still dont get what it did wrong... i did what you said here.


I don't get the question!

Do the extra 3 people join at the end of each two week period? If so, presumably we don't pay anything to the ones that join at the end of the 26th week, since we're only working out the cost for 26 weeks.
Reply 5
Original post by TeeEm
I suggest you write all the 14 terms out without (...)


Okay i wrote them out with the (...) and used the info from there and got the exact same answer as ive always been getting...:confused::bawling:
Reply 6
Original post by tiny hobbit
I don't get the question!

Do the extra 3 people join at the end of each two week period? If so, presumably we don't pay anything to the ones that join at the end of the 26th week, since we're only working out the cost for 26 weeks.


Thats right, at the end of each two week period; they start on the first day of the third week. If we make it 13 the answer will be even lower and my answer using 14 was too little. :frown:
Reply 7
Original post by Jmun
Okay i wrote them out with the (...) and used the info from there and got the exact same answer as ive always been getting...:confused::bawling:


what answer did you get?
I got 1,060,800
Reply 8
Original post by TeeEm
what answer did you get?
I got 1,060,800


I got the same but its wrong. The correct answer is $1 341 600
Reply 9
Original post by Jmun
I got the same but its wrong. The correct answer is $1 341 600


wrong says who?
Reply 10
Original post by TeeEm
wrong says who?


Uhhh the text book answers...
Reply 11
Original post by Jmun
Uhhh the text book answers...


well either the book or my modelling is wrong
I cannot make it any different
Maybe I am getting thick in my old age nowadays.
Reply 12
Original post by Jmun
Uhhh the text book answers...


Out of interest, which textbook is this?

And is it possible for you to upload a screenshot of the question, just so we can be sure we're not missing something?
Reply 13
Pure Mathematics 1 - Hugh Neil and Douglas Quading
Original post by Jmun
A woman started a business with a workforce of 50 people. Every two weeks the number of people in the workforce increased by 3 people.

a) How many people were there in the workforce after 26 weeks?

2 weeks = 3 more people
26 weeks = 13 additions so, 13 X 3 = 39 + 50 = 89. this was correct.

b) Each member of the workforce earned $600 per week. What was the total wage will for this 26 weeks?

My working:
$600 per person per week
first 2 weeks = 2 (600 X 50) = $60 000
so a is 60 000
Every 2 weeks, which can be said to be one addition as it is constant, 2 (3 X 600) = $3600 is added
So d is 3600
n is (26/2 + 1) = 14
Sum = n/2 (2a + (n-1)d)
= 7 (120 000 + (13)3600)
= $1 167 600
This is wrong. The correct answer is $1 341 600. What am I doing wrong???


b) Total wage bill =

Sn = 1/2n(an + a1) x 2 x 600

= 7(89 + 50) = 973 x 2 x 600 = 1,167,600

I get that too so original answer may be wrong.
(edited 8 years ago)

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