by Tiffany Santiago-Motta - Monday, 28 October 2024, 8:30 AM

Question

Number of replies: 1
Math Word Problem

Problem:

Tiffany is planning a DIY project in her home. She needs to buy paint for a room that measures 12 feet in length, 10 feet in width, and 8 feet in height. She wants to paint all four walls and the ceiling, but she will not be painting the floor or any windows.

How much area in square feet will she need to paint?
If one gallon of paint covers 350 square feet, how many gallons does she need to buy? (Assume she cannot purchase a partial gallon.)

Answer 1

To determine how much area Tiffany needs to paint, we'll first calculate the area of the four walls and the ceiling of the room.

1. Calculate the area of the four walls:

   • The room has two pairs of walls:

     • Two walls measuring 12 feet (length) x 8 feet (height)
     • Two walls measuring 10 feet (width) x 8 feet (height)

   • Area of the two 12-foot walls: $$2\times (12,\text{feet}\times 8,\text{feet})=2\times 96,\text{square feet}=192,\text{square feet}$$

   • Area of the two 10-foot walls: $$2\times (10,\text{feet}\times 8,\text{feet})=2\times 80,\text{square feet}=160,\text{square feet}$$

   • Total area of the walls: $$192,\text{square feet}+160,\text{square feet}=352,\text{square feet}$$

2. Calculate the area of the ceiling:

   • The ceiling measures 12 feet x 10 feet: $$12,\text{feet}\times 10,\text{feet}=120,\text{square feet}$$

3. Total area to be painted:

   • Total area (walls + ceiling): $$352,\text{square feet}+120,\text{square feet}=472,\text{square feet}$$

4. Determine the number of gallons of paint needed:

   • Each gallon of paint covers 350 square feet.
   • To find the number of gallons required: $$\frac{472,\text{square feet}}{350,\text{square feet per gallon}}\approx 1.34857$$
   • Since Tiffany cannot purchase a partial gallon, she will need to round up to the next whole number:
   • Therefore, she needs to buy 2 gallons of paint.

Final Answer: Tiffany needs to paint 472 square feet and should buy 2 gallons of paint.