The following are the steps involved in finding the value of x : y, if `(3x + 4y)/(2x + 5y) = 4/3`. Arrange them in sequential order from the first to the last.
1. `9x + 12y = 8x + 20 y`
2. Given, `(3x + 4y)/(2x + 5y) = 4/3`
3. `x/y = 8 rArr x : y = 8:1`
4. `3(3x + 4y) = 2(2x + 5y)`
5. `x = 8y`

Options

A. `2 to 4 to 1 to 5 to 3`
B. `2 to 4 to 3 to 5 to 1`
C. `2 to 1 to 4 to 5 to 3`
D. `2 to 1 to 4 to 3 to 5`

Answer

To solve the equation \(\frac{3x + 4y}{2x + 5y} = \frac{4}{3}\) and find the ratio \(x : y\), we can follow these steps in sequential order:

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ \frac{3x + 4y}{2x + 5y} = \frac{4}{3} \]
This is our starting point.

2. **Cross-multiply to eliminate the fraction:**
\[ 3(3x + 4y) = 4(2x + 5y) \]
This step allows us to work with a linear equation without fractions.

3. **Expand both sides:**
\[ 9x + 12y = 8x + 20y \]
Here, we distribute the constants to the terms inside the parentheses.

4. **Rearrange the equation to group like terms:**
\[ 9x - 8x = 20y - 12y \]
This simplifies to:
\[ x = 8y \]

5. **Express the ratio \(x : y\):**
\[ \frac{x}{y} = 8 \implies x : y = 8 : 1 \]

### Sequential Order of Steps:
- **Step 2:** Given, \(\frac{3x + 4y}{2x + 5y} = \frac{4}{3}\)
- **Step 4:** \(3(3x + 4y) = 2(2x + 5y)\)
- **Step 1:** \(9x + 12y = 8x + 20y\)
- **Step 5:** \(x = 8y\)
- **Step 3:** \(\frac{x}{y} = 8 \implies x : y = 8 : 1\)

### Final Arrangement:
The correct sequential order of steps is: **2, 4, 1, 5, 3.**