What is the solution to the linear equation?
[tex]+p=\frac{4}{5}+\frac{3}{5} p[/tex]
Answer (1)
Substitute each given value of p into the equation.
Check if the equation holds true for each value.
Find that p = 2 satisfies the equation p = 5 4 + 5 3 p .
Conclude that the solution is 2 .
Explanation
Problem Analysis We are given the linear equation p = 5 4 + 5 3 p and four possible solutions for p : 1, 2, 8, and 10. Our goal is to determine which of these values satisfies the given equation.
Solution Strategy To find the correct solution, we will substitute each given value of p into the equation and check if the equation holds true.
Testing the Options Let's test each option:
If p = 1 , then the equation becomes 1 = 5 4 + 5 3 ( 1 ) = 5 4 + 5 3 = 5 7 . Since 1 = 5 7 , p = 1 is not a solution.
If p = 2 , then the equation becomes 2 = 5 4 + 5 3 ( 2 ) = 5 4 + 5 6 = 5 10 = 2 . Since 2 = 2 , p = 2 is a solution.
If p = 8 , then the equation becomes 8 = 5 4 + 5 3 ( 8 ) = 5 4 + 5 24 = 5 28 . Since 8 = 5 28 , p = 8 is not a solution.
If p = 10 , then the equation becomes 10 = 5 4 + 5 3 ( 10 ) = 5 4 + 5 30 = 5 34 . Since 10 = 5 34 , p = 10 is not a solution.
Conclusion After testing all the given options, we found that only p = 2 satisfies the equation p = 5 4 + 5 3 p .
Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items with a fixed price and a variable quantity. For example, if a taxi charges a fixed fee of $4/5 plus $3/5 per mile, the equation p = 5 4 + 5 3 p can determine the distance you can travel for a given amount p . Understanding how to solve these equations helps in making informed decisions in everyday situations.
