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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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14 Oct 2017, 08:12
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5% (low)

Question Stats:

89% (01:43) correct 11% (01:55) wrong based on 65 sessions

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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

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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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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

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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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 \$

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