Choosing Measurements for the Reading Corner
The school is fixing up a rectangular reading corner that is 15 feet long and 12 feet wide. The principal has two jobs: (1) install a new baseboard along the bottom of all four walls, leaving a 3-foot gap for the door; (2) put new carpet on the floor. Baseboard costs $4 per foot. Carpet costs $3 per square foot. A volunteer writes a shopping list: "Baseboard: 15 × 12 = 180 feet. Carpet: 2(15 + 12) = 54 square feet." The principal says the volunteer used the wrong measurement for at least one job. The volunteer also wonders whether the door gap should be subtracted from the carpet or the baseboard. The school has a budget of $500 for both jobs. They need to decide whether the budget is enough.
1. Identify the volunteer's error(s). Which measurement-perimeter or area-should be used for each job?
Read the worked answer
Baseboard runs along the edge of the room, so it uses perimeter, not area. The volunteer used area (15 × 12 = 180) for baseboard, which is wrong.
Carpet covers the floor, so it uses area, not perimeter. The volunteer used perimeter (2(15 + 12) = 54) for carpet, which is also wrong.
The two formulas were swapped.
2. Calculate the total cost and decide if $500 is enough.
Read the worked answer
Baseboard length: perimeter = 2(15 + 12) = 54 feet. Subtract the 3-foot door gap: 54 − 3 = 51 feet.
Baseboard cost: 51 × $4 = $204.
Carpet area: 15 × 12 = 180 square feet.
Carpet cost: 180 × $3 = $540.
Total cost: $204 + $540 = $744.
$744 is greater than $500, so the budget is not enough. They are over by $244.
3. The volunteer asks if the door gap should be subtracted from the carpet. How do you respond?
Read the worked answer
No. The door gap is an opening along the wall, so it affects the length of the baseboard, not the area of the floor. Carpet covers the floor area, which is still 15 × 12 = 180 square feet. Subtract the 3-foot gap from the baseboard length only.