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A garden center sells a certain grass seed in 5-pound bags at $13.85

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A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 03 Jul 2016, 11:17
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A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

A) $94.03
B) $96.75
C) $98.78
D) $102.07
E) $105.3

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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 03 Jul 2016, 11:31
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As it is evident that 25 pound bag gives the least possible cost of the grass . So , we should maximize the number of 25 pound bags .
Since , the customer should buy at least 65 pounds and at most 80 pounds . Therefore , the customer should buy 25*3 = 75 pounds .
Since , the customer can satisfy the weight requirement using the 25 pound bag , he need not buy any other bag size
Least possible cost of grass seed that customer will buy = 32.25 * 3 = 96.75 $
Answer B
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 04 Jul 2016, 00:09
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there can be 2 cases

1)25+25+10+5=$98.78 or
2)25+25+25=$96.75

2 one is less amount and satisfies criteria between 65-80.if there are more cases it will obviously be more than $100
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 04 Jan 2018, 01:01
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Any mechanism to solve it other than brute force?
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 08 Apr 2018, 12:47
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Bunuel
Is there a quick method to solve the problem ? It took a bit extra time to calculate
please help
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 08 Apr 2018, 13:47
chandan1988, see if it helps:

In terms of the weight of bags, we could write the following equation: 65 <= 5*a + 10*b + 25*c <= 80 or 13 <= a + 2*b + 5*c <= 80 (equation I)

In terms of the total cost (T) we could write: 13.85*a + 20.43*b + 32.33*c = T, for which we want to minimize the value of T.

The main problem is that we have (a, 2b, 5c) in the first equation, and (a, b, c) in the second. But, what if we just transform the variables in the second equation to (a, 2b, 5c)?

T = 13.85*a + (20.43/2)*(2b) + (32.25/5)*(5c) = 13.82*a + 10.215*(2b) + 6.45*(5c) (equation II)

Thus, now we have a system of two equations, for which is clear that best thing to do is maximize c.

In other words, to solve it more quickly, we must think what kind of bag is the cheapest in terms of $ per pound.
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink]

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New post 19 May 2018, 15:49
Bunuel wrote:
A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

A) $94.03
B) $96.75
C) $98.78
D) $102.07
E) $105.3


This is a straight forward question with a straight-forward method to solve. However, a lot of time gets eaten up while solving and eliminating wrong answers. What time-efficient method do you suggest solving this problem? Or is the key simply to recognize 25 lb. bags gives us the "most bang for our buck" before we start our calculations, so we should know to solve for as much 25 lb. bags needed to meet the weight requirement?

(i hope my question makes sense)
Re: A garden center sells a certain grass seed in 5-pound bags at $13.85   [#permalink] 19 May 2018, 15:49
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