Let's solve the problem step-by-step.
First, define the variables:
- Let the area painted brown be [tex]\( x \)[/tex] square meters.
- The area painted yellow is 3 times the area painted brown, which can be expressed as [tex]\( 3x \)[/tex] square meters.
- The total area of the wall is 4 square meters.
### Step 1: Formulate the equation for the total area
The total area of the wall is the sum of the areas painted brown and yellow:
[tex]\[ x + 3x = 4 \][/tex]
Combine like terms:
[tex]\[ 4x = 4 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 1 \][/tex]
### Step 2: Determine the areas painted brown and yellow
Since [tex]\( x = 1 \)[/tex], the area painted brown is:
[tex]\[ 1 \text{ square meter} \][/tex]
The area painted yellow is:
[tex]\[ 3x = 3 \times 1 = 3 \text{ square meters} \][/tex]
### Step 3: Answer each specific question
#### (a) What was the ratio of the area painted yellow to the area painted brown?
The ratio of the area painted yellow to the area painted brown is:
[tex]\[ \frac{\text{yellow}}{\text{brown}} = \frac{3}{1} = 3 \][/tex]
#### (b) What fraction of the total area of the wall was painted brown?
The fraction of the total area painted brown is:
[tex]\[ \frac{\text{area painted brown}}{\text{total area}} = \frac{1}{4} \][/tex]
#### (c) Find the area of the wall painted yellow
The area of the wall painted yellow is:
[tex]\[ 3 \text{ square meters} \][/tex]
### Summary
- The ratio of the area painted yellow to the area painted brown is 3.
- The fraction of the total area of the wall that was painted brown is [tex]\( \frac{1}{4} \)[/tex].
- The area of the wall painted yellow is 3 square meters.
