help ...work problem

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charmaine: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sun May 18, 2008 11:04 pm; Thanked: 1 times

help ...work problem

by charmaine » Fri Oct 17, 2008 11:38 pm

A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

ans . 30

i can get answer by back solving ....but does anyone knows the linear equation .....i cant get it tho ....thanks thanks

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Source: Beat The GMAT — Problem Solving | Fri Oct 17, 2008 11:38 pm

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 am; Thanked: 36 times; Followed by:1 members

Re: help ...work problem

by Morgoth » Sat Oct 18, 2008 1:06 am

charmaine wrote:A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

ans . 30

i can get answer by back solving ....but does anyone knows the linear equation .....i cant get it tho ....thanks thanks

Cost of x calculators = 300

avg. cost of 1 calculator = 300/x

SP of 1 calculator = 5 +300/x
SP of x-2 calculators = (5+300/x)*(x-2)

SP - CP = 120

(5+300/x)*(x-2) - 300 = 120

(5+300/x)*(x-2)= 120 + 300

5x -10 + 300 - 600/x = 120 + 300

5x -600/x = 130

5x^2 - 600 = 130x

x^2 - 26x -120 = 0

(x-30) ( x+4) = 0

x = 30

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 » Sat Oct 18, 2008 1:16 am

1)CP of shipment = 300
quantity of calci= x
CP of one calci = 300/x

2)SP of shipment = 420 ( 120 more than CP)
quantity of calci for = x-2 ( 2 for demonstration)
left for selling

fro 1 and 2,

(300/x + 5 ) (x-2) = 420
solving we get,,,

x^2 - 26x - 120=0

we get factors 30 and -4

ans = 30
thus 30 pieces of calci.
u can substittute back in d question to confirm ur answer,

thanks,