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# Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and  [#permalink]

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22 Jan 2018, 01:29
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Difficulty:

55% (hard)

Question Stats:

63% (02:37) correct 37% (02:28) wrong based on 50 sessions

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Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and \$0.30 per 10 sheets. If one needs to purchase exactly 5640 sheets of paper, what the lowest possible price one must pay?

A. \$119.20
B. \$114.20
C. \$110.20
D. \$85.20
E. \$56.20

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Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and  [#permalink]

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22 Jan 2018, 05:06
Bunuel wrote:
Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and \$0.30 per 10 sheets. If one needs to purchase exactly 5640 sheets of paper, what the lowest possible price one must pay?

A. \$119.20
B. \$114.20
C. \$110.20
D. \$85.20
E. \$56.20

\$10 per pack of 500 i.e Price of 1 sheet of paper = 10*100/500 = 2 cents

\$3 per pack of 200 i.e Price of 1 sheet of paper = 3*100/200 = 1.5 cents

\$0.3 per pack of 10 i.e Price of 1 sheet of paper = 0.3*100/10 = 3 cents

Cheapest paper is purchased when pack of 200 is bought @\$3 per pack

Total Sheets to be purchased = 5640

i.e. Pack of 200 in 5640 sheets = 28 packs and 4 sheets left

Price of 28 packs of 200 sheets each pack = 28*\$3 = \$84

Price of 40 sheets @\$0.3 per 10 sheets = 0.3*4 = \$1.2

Total Price of 5640 sheets = \$84+\$1.2 = \$85.2

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Re: Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and  [#permalink]

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23 Jan 2018, 08:56
Bunuel wrote:
Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and \$0.30 per 10 sheets. If one needs to purchase exactly 5640 sheets of paper, what the lowest possible price one must pay?

A. \$119.20
B. \$114.20
C. \$110.20
D. \$85.20
E. \$56.20

Let’s calculate the unit (per sheet) cost of each option:

Packs of 500: unit cost = \$10/500 = \$0.02

Packs of 200: unit cost = \$3/200 = \$0.015

Single sheets: unit cost = \$0.30/10 = \$0.03

We see that the greatest savings occurs with packs of 200, then packs of 500, and, finally, single sheets.

Thus, to maximize savings, we should buy as many packs of 200 as possible. Since 5640/200 = 28.2, we can buy 28 packs of 200, which will cost us:

\$3 x 28 = \$84

So now we have 5640 - (28 x 200) = 40 sheets left. For these 40 sheets, we must buy them as single sheets, and they will cost us:

\$0.03 x 40 = \$1.20

Thus, the lowest possible price we have to pay is \$84 + \$1.20 = \$85.20.

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Re: Paper can be purchased for \$10 per pack of 500, \$3 per pack of 200 and   [#permalink] 23 Jan 2018, 08:56
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