There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is `3 : 1`. How many more girls should be added to the council so that the ratio of number of boys to the number of girls may be `9 : 5` ?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given information
We know that there are 36 members in total in the student council, and the ratio of boys to girls is given as \(3:1\).

### Step 2: Set up the equations based on the ratio
Let the number of boys be \(3x\) and the number of girls be \(x\). According to the ratio, we can express the total number of members as:
\[ 3x + x = 36 \]

### Step 3: Solve for \(x\)
Combine the terms on the left:
\[ 4x = 36 \]
Now, divide both sides by 4:
\[ x = \frac{36}{4} = 9 \]

### Step 4: Calculate the number of boys and girls
Now that we have \(x\), we can find the number of boys and girls:
- Number of boys = \(3x = 3 \times 9 = 27\)
- Number of girls = \(x = 9\)

### Step 5: Set up the new ratio requirement
We need to find how many more girls (\(y\)) should be added so that the new ratio of boys to girls becomes \(9:5\). The new number of girls will be \(9 + y\).

### Step 6: Set up the equation for the new ratio
According to the new ratio:
\[ \frac{27}{9 + y} = \frac{9}{5} \]

### Step 7: Cross-multiply to solve for \(y\)
Cross-multiplying gives us:
\[ 27 \times 5 = 9 \times (9 + y) \]
This simplifies to:
\[ 135 = 81 + 9y \]

### Step 8: Isolate \(y\)
Subtract 81 from both sides:
\[ 135 - 81 = 9y \]
\[ 54 = 9y \]
Now, divide both sides by 9:
\[ y = \frac{54}{9} = 6 \]

### Step 9: Conclusion
Therefore, the number of girls that should be added to the council is \(6\).

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