What is the value of `p` if
`(p)/(2)+3q=6 and 2p-2q=10 ?`

Options

A. 1
B. 4
C. 6
D. 16

Answer

To find the value of \( p \) from the given equations:

1. **Write down the equations:**
\[ \frac{p}{2} + 3q = 6 \quad \text{(Equation 1)} \]
\[ 2p - 2q = 10 \quad \text{(Equation 2)} \]

2. **Simplify Equation 2:**
Divide the entire Equation 2 by 2 to make it simpler:
\[ p - q = 5 \quad \text{(Equation 2 simplified)} \]

3. **Express \( q \) in terms of \( p \):**
From the simplified Equation 2, we can express \( q \):
\[ q = p - 5 \quad \text{(Equation 3)} \]

4. **Substitute Equation 3 into Equation 1:**
Replace \( q \) in Equation 1 with the expression from Equation 3:
\[ \frac{p}{2} + 3(p - 5) = 6 \]

5. **Distribute and simplify:**
\[ \frac{p}{2} + 3p - 15 = 6 \]
Combine like terms:
\[ \frac{p}{2} + 3p = 6 + 15 \]
\[ \frac{p}{2} + 3p = 21 \]

6. **Convert \( 3p \) to a fraction:**
To combine \( \frac{p}{2} \) and \( 3p \):
\[ 3p = \frac{6p}{2} \]
Thus,
\[ \frac{p}{2} + \frac{6p}{2} = 21 \]
\[ \frac{7p}{2} = 21 \]

7. **Solve for \( p \):**
Multiply both sides by 2 to eliminate the fraction:
\[ 7p = 42 \]
Divide by 7:
\[ p = 6 \]

**Final Answer:**
\[ p = 6 \]

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