Question

ngrid needs to paint her bedroom walls. The room is 9 feet tall by 12 feet wide and 11 feet long. It has a door that is 7 feet tall by 3.5 feet wide and two windows 3.5 feet by 3.5 feet that don't need paint.



How many gallons of paint should Ingrid buy if 1 gallon covers 102 square feet?

Answer 1

To determine how many gallons of paint Ingrid needs, we'll first calculate the total wall area to be painted, subtract the areas that don't need paint (the door and windows), and then find out how many gallons are necessary based on the coverage per gallon.

### Step 1: Calculate Total Wall Area

Ingrid's bedroom has four walls. The dimensions of the room are:

- Height: 9 feet
- Width: 12 feet
- Length: 11 feet

The area for the two long walls (each 11 feet long) is:
\[
2 \times (9 \text{ feet height} \times 11 \text{ feet length}) = 2 \times 99 = 198 \text{ square feet}
\]

The area for the two short walls (each 12 feet wide) is:
\[
2 \times (9 \text{ feet height} \times 12 \text{ feet width}) = 2 \times 108 = 216 \text{ square feet}
\]

Now, add the area of the four walls together:
\[
198 \text{ square feet} + 216 \text{ square feet} = 414 \text{ square feet}
\]

### Step 2: Calculate the Areas Not to be Painted

Next, we need to calculate the areas of the door and the two windows.

**Door area:**
\[
7 \text{ feet height} \times 3.5 \text{ feet width} = 24.5 \text{ square feet}
\]

**Window area (for two windows):**
\[
2 \times (3.5 \text{ feet height} \times 3.5 \text{ feet width}) = 2 \times 12.25 = 24.5 \text{ square feet}
\]

### Step 3: Calculate Total Area Not to be Painted

Now, let's add the areas of the door and the windows:
\[
24.5 \text{ square feet (door)} + 24.5 \text{ square feet (windows)} = 49 \text{ square feet}
\]

### Step 4: Calculate the Total Area to be Painted

Now, we subtract the area that does not need painting from the total wall area:
\[
414 \text{ square feet (total walls)} - 49 \text{ square feet (door and windows)} = 365 \text{ square feet}
\]

### Step 5: Calculate the Number of Gallons Needed

Given that 1 gallon of paint covers 102 square feet, we can find out how many gallons are needed:
\[
\text{Number of gallons} = \frac{365 \text{ square feet}}{102 \text{ square feet per gallon}} \approx 3.58
\]

Since Ingrid cannot buy a fraction of a gallon, she needs to round up to the next whole number:
\[
\text{Gallons of paint required} = 4
\]

Thus, Ingrid should buy **4 gallons of paint**.