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The length of the rectangular playroom in Sheila's basement is 1½ times its width. The room has no windows and has a height of 8 feet. Sheila has decided to wallpaper the entire room and put a border over the wallpaper at the top around the room. To determine how much wallpaper is needed, she has to add together the area of each wall to get the total surface area of the room. The door to this room measures 2.5 feet wide by 6.5 feet high and will not need wallpaper.

A) Let x be the width of the room. Write and simplify an equation in terms of x to determine the total surface area (S) of the playroom's walls.

B) The playroom is 12 feet wide. Each roll of wallpaper will cover approximately 56 square feet. The wallpaper has no pattern; therefore, it is not necessary to allow for matching patterns when calculating the amount of wallpaper to purchase. What is the least number of rolls Sheila will need to paper her room? Show your work.

C) Sheila plans to spend no more than $350.00 (ignore tax) on the wallpaper and border. The border costs $19.97 per 10-yard roll. The border will be pasted onto the wallpaper at the top of each wall with no overlap. Explain how to determine the most expensive wallpaper Sheila can buy while staying within her budget.

Materials/Resources:

  • Calculator
  • HSPA Mathematics Reference Sheet

Techniques for PAT Scoring:
See item-specific sample response and scoring rubric C1006-008R for this PAT.


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