If 45% of 30 + 2X = 35% of 15 + 20% of 45, then the value of X is:

Options

A. `1/9`
B. `3/5`
C. `2/7`
D. `3/8`

Answer

To solve the equation \( 45\% \text{ of } 30 + 2X = 35\% \text{ of } 15 + 20\% \text{ of } 45 \), we will follow these steps:

### Step 1: Convert percentages to fractions
Convert the percentages to fractions for easier calculation:
- \( 45\% = \frac{45}{100} \)
- \( 35\% = \frac{35}{100} \)
- \( 20\% = \frac{20}{100} \)

### Step 2: Write the equation with fractions
Now substitute these fractions into the equation:
\[ \frac{45}{100} \times 30 + 2X = \frac{35}{100} \times 15 + \frac{20}{100} \times 45 \]

### Step 3: Calculate the left side
Calculate \( \frac{45}{100} \times 30 \):
\[ \frac{45 \times 30}{100} = \frac{1350}{100} = 13.5 \]
So, the left side becomes:
\[ 13.5 + 2X \]

### Step 4: Calculate the right side
Calculate \( \frac{35}{100} \times 15 \) and \( \frac{20}{100} \times 45 \):
\[ \frac{35 \times 15}{100} = \frac{525}{100} = 5.25 \]
\[ \frac{20 \times 45}{100} = \frac{900}{100} = 9 \]
Now, add these two results:
\[ 5.25 + 9 = 14.25 \]

### Step 5: Set up the equation
Now we have the equation:
\[ 13.5 + 2X = 14.25 \]

### Step 6: Isolate \( 2X \)
Subtract \( 13.5 \) from both sides:
\[ 2X = 14.25 - 13.5 \]
\[ 2X = 0.75 \]

### Step 7: Solve for \( X \)
Divide both sides by 2:
\[ X = \frac{0.75}{2} = \frac{75}{200} = \frac{3}{8} \]

### Final Answer
Thus, the value of \( X \) is \( \frac{3}{8} \).

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