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A wall with no windows is 11 feet high and 20 feet long. A large roll

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A wall with no windows is 11 feet high and 20 feet long. A large roll [#permalink]

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A wall with no windows is 11 feet high and 20 feet long. A large roll of wallpaper costs $25 and will cover 60 square feet of wall. A small roll of wallpaper costs $6 and will cover 10 square feet of wall. What is the least cost for enough wallpaper to cover the wall?

(A) $75
(B) $99
(C) $100
(D) $120
(E) $132
[Reveal] Spoiler: OA

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A wall with no windows is 11 feet high and 20 feet long. A large roll [#permalink]

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New post 14 Oct 2017, 10:11
Bunuel wrote:
A wall with no windows is 11 feet high and 20 feet long. A large roll of wallpaper costs $25 and will cover 60 square feet of wall. A small roll of wallpaper costs $6 and will cover 10 square feet of wall. What is the least cost for enough wallpaper to cover the wall?

(A) $75
(B) $99
(C) $100
(D) $120
(E) $132

The wall's area is 11 * 20 = 220 sq ft

There are two options: the exact amount of wallpaper, or more wallpaper than is needed.

Option 1: combination of rolls that cover different amounts of square feet

If exact:
3 rolls * 60 sq ft each = 180 sq ft, which means
(220-180) = 40 sq ft remain to be covered

40 sq ft/10 sq ft = 4 rolls: to cover the rest would take 4 rolls of 10 sq ft each

Cost, Option 1:
(3 * $25) = $75
(4 * $6) = $24
Total Cost = $99

Option 2: the price per square foot is lower for the larger rolls. Often we can buy too much of the cheaper per unit cost item and still save money.

Option 2: only rolls that cover 60 square feet

Three rolls that cover 60 square feet are not enough.
(3 * 60) = 180 sq ft

Total (220-180) = 40 sq ft remain

It would take one more of the roll that covers 60 sq ft to make up the difference (in fact more than make up the difference - there would be extra wallpaper)

4 * 60 = 240 sq ft
Cost: 4 * $25 = $100

Option 1 is cheaper.

The least cost for enough wallpaper to cover the wall is $99

Answer B

P.S. Answer A can be eliminated.
It can't be only smaller rolls of 10 sq ft @ $6/roll. $75 is not a multiple of $6.

As above, three larger rolls cost $75 total, and three rolls are not enough.

Finally, a combination produces these possible numbers
1 large roll + 16 small = $180
2 large + 10 small = $150

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Re: A wall with no windows is 11 feet high and 20 feet long. A large roll [#permalink]

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New post 14 Oct 2017, 21:57
Bunuel wrote:
A wall with no windows is 11 feet high and 20 feet long. A large roll of wallpaper costs $25 and will cover 60 square feet of wall. A small roll of wallpaper costs $6 and will cover 10 square feet of wall. What is the least cost for enough wallpaper to cover the wall?

(A) $75
(B) $99
(C) $100
(D) $120
(E) $132


Area of wall = 11*20 = 220 square feet
Cost of large roll of wallpaper that covers 60 square feet = 25$
Cost of small roll of wallpaper that covers 10 square feet = 6$
Cost of small roll of wallpaper to cover 60 square feet = 6*6 = 36$

So , to minimize total cost we should maximise the use the large roll.
220 = 60*3 + 10*4 ( Max number of large rolls = 3)

Therefore minimum cost = 25*3 + 6*4 = 99 $

Answer B
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Re: A wall with no windows is 11 feet high and 20 feet long. A large roll   [#permalink] 14 Oct 2017, 21:57
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