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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