2 ways to pay dues

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jessicamuniz: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jul 17, 2008 1:02 pm

2 ways to pay dues

by jessicamuniz » Wed Nov 05, 2008 7:06 am

Hi everybody:
I am actually looking for some help to answer this one.

A certain union has 60 members. There are exactly two ways for members to pay dues: anually and quarterly. One-third of the members pays dues anually, and the rest pay quarterly. A single quarterly dues payment is equal to two-ninths of anual dues payments. If the total recevied by the union in dues is $10,000 for a given year, what was the total amount received in due payments from the memebers who paid anually?

Looking for hearing some possible solutions, thanks

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Source: Beat The GMAT — Problem Solving | Wed Nov 05, 2008 7:06 am

Fab: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Tue Jul 15, 2008 10:23 am; Location: Lima; Thanked: 4 times; Followed by:1 members

by Fab » Wed Nov 05, 2008 8:15 am

Hi Jessica,

First of all, 20 people pays anually and 40 people pays quarterly.
Then, a quarter pay is equal to 2/9 an anual pay, so Q = 2/9A.
There are 4 quarters in a year so total quarter pays are equal to: 4*(2/9A).
Finally, 20A + 40*4*(2/9)A = 10,000
Solving: 180A +320A=90,000 ----->A= 108
So, 180$ * 20(people) = $3,600

Hope it helps.

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bjp2008: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Tue Sep 30, 2008 6:36 am

Re: 2 ways to pay dues

by bjp2008 » Wed Nov 05, 2008 8:16 am

jessicamuniz wrote:Hi everybody:
I am actually looking for some help to answer this one.

A certain union has 60 members. There are exactly two ways for members to pay dues: anually and quarterly. One-third of the members pays dues anually, and the rest pay quarterly. A single quarterly dues payment is equal to two-ninths of anual dues payments. If the total recevied by the union in dues is $10,000 for a given year, what was the total amount received in due payments from the memebers who paid anually?

Looking for hearing some possible solutions, thanks

Let x be the single annual pay.

So, 10000 = 20*(2/9)*x + 40x
Solving gives x = 225.
Total recevied on annual payment = 225*(2/3)*60 = 9000
hope this helps

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raunekk: Legendary Member; Posts: 1159; Joined: Wed Apr 16, 2008 10:35 pm; Thanked: 56 times

by raunekk » Wed Nov 05, 2008 8:27 am

wats d OA??

i m getting a different one...

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jimmiejaz: Master | Next Rank: 500 Posts; Posts: 207; Joined: Sun Mar 11, 2007 6:16 pm; Location: Mumbai; Thanked: 11 times

Re: 2 ways to pay dues

by jimmiejaz » Wed Nov 05, 2008 8:28 am

bjp2008 wrote:
jessicamuniz wrote:Hi everybody:
I am actually looking for some help to answer this one.

A certain union has 60 members. There are exactly two ways for members to pay dues: anually and quarterly. One-third of the members pays dues anually, and the rest pay quarterly. A single quarterly dues payment is equal to two-ninths of anual dues payments. If the total recevied by the union in dues is $10,000 for a given year, what was the total amount received in due payments from the memebers who paid anually?

Looking for hearing some possible solutions, thanks
Let x be the single annual pay.

So, 10000 = 20*(2/9)*x + 40x
Solving gives x = 225.
Total recevied on annual payment = 225*(2/3)*60 = 9000
hope this helps

Hi bjp2008,

u have taken the opposite of wat you supposed mate...
btw, the ans given by fab is correct. i am also getting 3600.
Whats the original answer???

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

Re: 2 ways to pay dues

by logitech » Wed Nov 05, 2008 8:47 am

jessicamuniz wrote:Hi everybody:
I am actually looking for some help to answer this one.

A certain union has 60 members. There are exactly two ways for members to pay dues: anually and quarterly. One-third of the members pays dues anually, and the rest pay quarterly. A single quarterly dues payment is equal to two-ninths of anual dues payments. If the total recevied by the union in dues is $10,000 for a given year, what was the total amount received in due payments from the memebers who paid anually?

Looking for hearing some possible solutions, thanks

Okay there is a little bit confusion here:

20 Members Annualy

40 Members Quarterly

A single quarterly dues payment is equal to two-ninths of anual dues payments.

2/9 x 4 = 8/9 Annual

So actually if you choose to pay quarterly, you will pay less