A gallon of latex paint can cover 400 square feet.  Maria has a rectangular room whose dimensions are 11 feet by 21 ​feet, with 10​-foot ceilings.  How many gallon containers of paint does she need to buy to paint two coats on each​ wall?

To solve this problem, we need to calculate the total area of the walls that Maria needs to paint, and then determine how many gallons of paint are required for two coats.

### Step 1: Calculate the total area of the walls
The room has four walls. Two of the walls have dimensions 11 feet by 10 feet (height), and the other two walls have dimensions 21 feet by 10 feet (height).

- **Area of the two 11-foot walls**:
  \[
  2 \times (11 \text{ feet} \times 10 \text{ feet}) = 2 \times 110 \text{ square feet} = 220 \text{ square feet}
  \]

- **Area of the two 21-foot walls**:
  \[
  2 \times (21 \text{ feet} \times 10 \text{ feet}) = 2 \times 210 \text{ square feet} = 420 \text{ square feet}
  \]

- **Total area of the walls**:
  \[
  220 \text{ square feet} + 420 \text{ square feet} = 640 \text{ square feet}
  \]

### Step 2: Calculate the total area for two coats
Since Maria wants to apply two coats, we multiply the total area by 2:
\[
2 \times 640 \text{ square feet} = 1280 \text{ square feet}
\]

### Step 3: Determine how many gallons of paint are needed
One gallon of paint covers 400 square feet.

- **Number of gallons required**:
  \[
  \frac{1280 \text{ square feet}}{400 \text{ square feet per gallon}} = 3.2 \text{ gallons}
  \]

Since Maria can't buy a fraction of a gallon, she needs to round up to the nearest whole number. Thus, she needs to buy **4 gallons** of paint.

### Final Answer
Maria needs to buy **4 gallons** of paint.

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Would you like more details or have any other questions?

Here are some related questions to expand your understanding:
1. How would the number of gallons change if the room had 9-foot ceilings?
2. What if the room had a door that measured 3 feet by 7 feet? How would that affect the amount of paint needed?
3. How much paint would be required if Maria only wanted to paint one coat?
4. How would the calculation differ if the paint coverage per gallon was different, say 350 square feet per gallon?
5. How much paint would be needed if the room had one large window measuring 5 feet by 4 feet?

**Tip:** When calculating materials like paint, always consider rounding up since fractional quantities of physical goods are often impractical.

Discover how much paint Maria needs to buy for her room with dimensions 11 feet by 21 feet and 10-foot ceilings. Learn the step-by-step process to calculate the total wall area and determine the gallons of paint required for two coats. Suitable for students in Grades 6-8.

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