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For a shipment of n bottles of a certain product, a mail order firm ch

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For a shipment of n bottles of a certain product, a mail order firm ch [#permalink] New post   31 Oct 2023, 06:28
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For a shipment of n bottles of a certain product, a mail order firm charges a price of $40.00 per bottle, plus a shipping fee of 5 percent of the total price of the n bottles, plus a handling fee of $5.00 per shipment. What is the least value of n for which the total charge per bottle shipped is less than $42.50 ?

A) 26
B) 21
C) 18
D) 11
E) 6
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D
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For a shipment of n bottles of a certain product, a mail order firm ch [#permalink] New post   31 Oct 2023, 07:59
sourabhmulik wrote:
For a shipment of n bottles of a certain product, a mail order firm charges a price of $40.00 per bottle, plus a shipping fee of 5 percent of the total price of the n bottles, plus a handling fee of $5.00 per shipment. What is the least value of n for which the total charge per bottle shipped is less than $42.50 ?

A) 26
B) 21
C) 18
D) 11
E) 6


Each bottle has a fixed price of $40, hence other chargers, which include a 5% shipping fee and the handling fee should be equal to $2.50.

Hence, we can translate the question as -

What is the least value of n for which the shipping fee and handling fee are less than $2.50

Shipping Fee per bottle = \(5\)% of \(40\)

Handling Fee per bottle = \(\frac{5}{n}\)

\(5\)% of \(40 + \frac{5}{n} < 2.50\)

\(2 + \frac{5}{n} < 2.50\)

\(n > 10\)

Hence, least number = 11

Option D
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For a shipment of n bottles of a certain product, a mail order firm ch [#permalink] New post   13 Nov 2023, 04:03
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For a shipment of n bottles of a certain product, a mail order firm charges a price of $40.00 per bottle, plus a shipping fee of 5 percent of the total price of the n bottles, plus a handling fee of $5.00 per shipment. What is the least value of n for which the total charge per bottle shipped is less than $42.50 ?

A) 26
B) 21
C) 18
D) 11
E) 6


Good question.

Let the number of bottles be N.

Total cost be: T = \(40(N) + \frac{5}{100}*40(N) + 5\)

Asked for, when will \(\frac{T}{N} < 42.5\)? or When will \(T < 42.5N?\)

Equating the equations:

\(T < 42.5N?\)
\(40(N) + \frac{5}{100}*40(N) + 5 < 42.5N\)
\(42(N) + 5 < 42.5N\)
\(10 < N\)

The Answer is 11. D.
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Re: For a shipment of n bottles of a certain product, a mail order firm ch [#permalink] New post   20 Jan 2024, 13:45
Logic can be used to know the right answer.

With 5% tax, the charge per bottle is $42 excluding shipping.

Shipping is $5 irrespective of the number of bottles..

The shipment charges for 10 bottles is 50 cent or $0.50 per bottle.
For 10 bottles, the total charge per bottle is $42.50.

For 11 bottles, the shipping charges per bottle is less than $0.50.

Therefore for 11 bottles and more, the total charges is less than $42.50 per bottle.

Therefore option D is the answer.
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Re: For a shipment of n bottles of a certain product, a mail order firm ch [#permalink]
20 Jan 2024, 13:45
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