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A merchant paid $300 for a shipment of x identical

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A merchant paid $300 for a shipment of x identical [#permalink]

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New post 21 Apr 2012, 21:18
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74% (02:30) correct 26% (04:34) wrong based on 226 sessions

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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?

A. 24
B. 25
C. 26
D. 28
E. 30

Is this question correct? Shipping cost given but cost of each calculator missing.....
[Reveal] Spoiler: OA

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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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New post 21 Apr 2012, 23:03
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boomtangboy 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?

A. 24
B. 25
C. 26
D. 28
E. 30

Is this question correct? Shipping cost given but cost of each calculator missing.....


"A merchant paid $300 for a shipment of x identical calculators" means that there was a shipment of x calculators which cost merchant $300.

The average cost of each calculator is \(\frac{300}{x}\);
The average price of each calculator is \(\frac{300}{x}+5\);
Number of calculators sold is \(x-2\);
The total revenue is \(300+120=420\);

So, \((x-2)*(\frac{300}{x}+5)=420\). At this point it's better to substitute values. Answer choice E fits: \((30-2)*(\frac{300}{30}+5)=28*15=420\).

Answer: E.

Hope it's clear.
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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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New post 04 Oct 2013, 13:21
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Try plugging in the answer:-
1st Try selecting options which are divisible by 300
If you select 30 as x.Therefore avg cost of each calculator 300/30 i.e 10$.
Set aside 2 .So we have 28 calc.
Each calc sold at 5$ more i.e 10+5=15$ & 15x28=$420
Difference is $420-$300=120
E) is the answer hope it helps :)

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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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New post 11 Jan 2014, 08:52
boomtangboy 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?

A. 24
B. 25
C. 26
D. 28
E. 30

Is this question correct? Shipping cost given but cost of each calculator missing.....


I'd go with backsolving on this one though I must admit that originally I tried to solve algebraically and was stuck with variables and quadratics

We will have (300/x + 5)(x-2) = 420

Then begin replacing, I started with 25 cause 26 would not yield an integer when divided by 300 but it didn't work, so I realized I needed a bigger number and the only factor of 30 that could work was E

So E

Hope it helps
Cheers!
J :)

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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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New post 11 Jan 2014, 11:29
Cost of calculator=300/x
Given,(x-2)(300/x +5)=420
We can check by options that only x=30 satisfies this equation.
Hence,
Ans. E

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A merchant paid $300 for a shipment of x identical [#permalink]

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New post 20 Mar 2014, 14:07
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?
A. 24
B. 25
C. 26
D. 28
E. 30

Last edited by MacFauz on 20 Mar 2014, 22:25, edited 1 time in total.
Edited title and added OA

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Re: Word Problem [#permalink]

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New post 20 Mar 2014, 19:56
Answer = E

Total Calculators = x

Cost per calculator = \(\frac{300}{x}\)

Calculators sold = x-2

Selling price per calculator = \(\frac{300}{x} +5\)

Total amount received = \((\frac{300}{x} + 5) * (x-2) = 420\)

Solving,

\(x^2 - 26x - 120 = 0\)

x = 30
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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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New post 21 Mar 2014, 02:51
SomIyer 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?
A. 24
B. 25
C. 26
D. 28
E. 30


Merging similar topics. Please refer to the discussion above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3, 5, and 7. Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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Re: A merchant paid $300 for a shipment of x identical [#permalink]

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New post 15 Sep 2017, 22:48
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Re: A merchant paid $300 for a shipment of x identical   [#permalink] 15 Sep 2017, 22:48
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