Understanding the Equation
To solve the equation \( \frac{20p}{3} = 40 \), we need to isolate the variable \( p \). This equation states that twenty-thirds of \( p \) equals 40.
Step 1: Eliminate the Fraction
- To eliminate the fraction, multiply both sides of the equation by 3:
3 * \( \frac{20p}{3} \) = 3 * 40
- The equation simplifies to:
20p = 120
Step 2: Isolate p
- Now, divide both sides by 20 to solve for \( p \):
\( p = \frac{120}{20} \)
- This simplifies to:
p = 6
Final Solution
- The value of \( p \) is 6.
Verification
- To confirm our solution, substitute \( p \) back into the original equation:
\( \frac{20(6)}{3} = 40 \)
- Simplifying the left side:
\( \frac{120}{3} = 40 \)
- Since both sides are equal, our solution is verified.
Conclusion
- The solution to the equation \( \frac{20p}{3} = 40 \) is \( p = 6 \). This method demonstrates how to manipulate algebraic equations to find the value of a variable effectively.