Math Problem Statement

A gallon of latex paint can cover 300 square feet. Maria has a rectangular room whose dimensions are 16 feet by 25 ​feet, with 8​-foot ceilings. How many gallon containers of paint does she need to buy to paint two coats on each​ wall?

Solution

To determine how many gallons of paint Maria needs, let's break down the problem step by step.

Step 1: Calculate the total wall area to be painted

Maria's room has four walls, two of which are 16 feet wide and 8 feet tall, and the other two are 25 feet wide and 8 feet tall.

  • Area of two 16-foot by 8-foot walls: 2×(16×8)=2×128=256 square feet2 \times (16 \times 8) = 2 \times 128 = 256 \text{ square feet}

  • Area of two 25-foot by 8-foot walls: 2×(25×8)=2×200=400 square feet2 \times (25 \times 8) = 2 \times 200 = 400 \text{ square feet}

  • Total wall area: 256+400=656 square feet256 + 400 = 656 \text{ square feet}

Step 2: Calculate the total area for two coats of paint

Since Maria needs to paint two coats:

656×2=1312 square feet656 \times 2 = 1312 \text{ square feet}

Step 3: Determine the number of gallons required

Each gallon of paint covers 300 square feet.

13123004.37\frac{1312}{300} \approx 4.37

Since Maria cannot buy a fraction of a gallon, she will need to round up to the next whole number.

Final Answer:

Maria needs to buy 5 gallons of paint to cover the walls with two coats.


Do you want more details or have any questions about this solution? Here are some related questions you might find useful:

  1. How would the number of gallons change if the ceiling height was different?
  2. What if Maria wanted to paint the ceiling as well?
  3. How many gallons would be needed for a single coat of paint?
  4. How does the paint coverage change if she uses a different type of paint with different coverage per gallon?
  5. What if there were windows or doors in the room that reduced the wall area?

Tip: When painting, always buy slightly more paint than calculated to ensure you have enough for touch-ups.

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Math Problem Analysis

Mathematical Concepts

Geometry
Measurement
Arithmetic

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8