Algebra lunch

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Lookingfor700GMAT: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Mon Feb 08, 2010 12:41 pm

by Lookingfor700GMAT » Wed Mar 10, 2010 9:33 am

To celebrate a colleague's retirement, the T coworkers in an office agreed to equally share the cost of a catered lunch. If the lunch cost a total of x dollars and S of the coworkers, fail to pay their share, what is the expression which represents the additional amount in dollars that each of the remaining coworkers would need to contribute so that cost of the lunch is completely paid?

Please explain how the below answer is found.

The answer is Sx/ T(T-S)

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Source: Beat The GMAT — Problem Solving | Wed Mar 10, 2010 9:33 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Wed Mar 10, 2010 7:47 pm

Lookingfor700GMAT wrote:To celebrate a colleague's retirement, the T coworkers in an office agreed to equally share the cost of a catered lunch. If the lunch cost a total of x dollars and S of the coworkers, fail to pay their share, what is the expression which represents the additional amount in dollars that each of the remaining coworkers would need to contribute so that cost of the lunch is completely paid?

Please explain how the below answer is found.

The answer is Sx/ T(T-S)

total payment=x
total workers=t
per head cost=x/t(original cost)

new strength of workers sharing the cost=t-s
per head=x/(t-s)[increased cost ]

now additional cost for wokers is= increased cost - original cost
=x/(t-s)-x/t=sx/[t(t-x)]

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harsh001: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Mar 12, 2010 2:51 am

by harsh001 » Sat Mar 13, 2010 2:13 am

This problem is best solved by using numbers ok:

Now let T (Total Co-workers) = 10
X (Cost of lunch) = 100
S (Co-workers who refuse to pay) = 5

Now:
Cost per worker = X/T = 100/10 = 10
Actual amount paid by workers willing to pay = 100/(10-5) = 20
Therefore additional amount paid by workers who paid = 20 - 10 = 10(a)

SX/T(T-S) = 5*100/10(10-5) = 500/50 = 10(a)

(a) = (a) therefore SX/T(T-S) is correct!!

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Mar 13, 2010 2:34 am

Lookingfor700GMAT wrote:To celebrate a colleague's retirement, the T coworkers in an office agreed to equally share the cost of a catered lunch. If the lunch cost a total of x dollars and S of the coworkers, fail to pay their share, what is the expression which represents the additional amount in dollars that each of the remaining coworkers would need to contribute so that cost of the lunch is completely paid?

Please explain how the below answer is found.

The answer is Sx/ T(T-S)

When T coworkers were to equally share in $x, each should have contributed $x/T. If S (assumably < T) of the coworkers fail to pay their share, the $x must be equally shared by (T - S) coworkers and each would now have contributed $x/(T - S). Hence, the additional amount in dollars that each of the remaining coworkers would need to contribute

= ${x/(T - S) - (x/T)}

= ${S x/ T (T - S)}

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