The root of the equation `3/4 p + 8=17 is "_______"`

Options

A. 5
B. 12
C. 20
D. 11

Answer

To solve the equation \( \frac{3}{4}p + 8 = 17 \) for \( p \), we can follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ \frac{3}{4}p + 8 = 17 \]

### Step 2: Isolate the term with \( p \)
To isolate the term with \( p \), we need to eliminate the constant on the left side. We can do this by subtracting 8 from both sides of the equation:
\[ \frac{3}{4}p + 8 - 8 = 17 - 8 \]
This simplifies to:
\[ \frac{3}{4}p = 9 \]

### Step 3: Eliminate the fraction
Next, we want to solve for \( p \). Since \( \frac{3}{4}p \) means \( p \) is multiplied by \( \frac{3}{4} \), we can eliminate the fraction by multiplying both sides of the equation by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):
\[ p = 9 \times \frac{4}{3} \]

### Step 4: Perform the multiplication
Now we calculate \( 9 \times \frac{4}{3} \):
\[ p = \frac{9 \times 4}{3} = \frac{36}{3} = 12 \]

### Final Answer
Thus, the root of the equation is:
\[ p = 12 \]

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