Solving for Peters Salary Using Proportions
Understanding how to solve salary-related problems using proportions is a valuable skill, especially in a professional setting. This article will walk you through a specific problem where we need to find Peters salary based on the given proportions and Mary's salary. We will demonstrate several methods to arrive at the solution and explore the underlying mathematical principles.
Problem Statement
The question at hand asks, 'If 3/4 of Peters salary is equal to 2/4 of Marys salary, and Marys salary is 120000, what is Peters salary?' Let's break this down step by step.
Mathematical Formulation
Using the information given, we can set up the following premise and assumptions:
Premise
3/4P2/4M
Assumptions
Mary's salary, M, is 120000 Peter's salary, P, in terms of M is 2/4MCalculation
Let's solve for Peter's salary with the given values. We start by substituting Mary's salary into the equation:
3/4P 2/4M
3/4P 2/4 * 120000
3/4P 60000
To find P, we can multiply both sides of the equation by 4/3:
P 60000 * 4/3
P 80000
Proof of Solution
To verify our solution, we can substitute P 80000 back into the original equation:
3/4 * 80000 2/4 * 120000
60000 60000
The equation checks out, confirming that Peter's salary is indeed 80000.
Alternative Methods
There are several ways to approach this problem. Here are a couple of additional methods:
Method 1
Since 3/4P 2/4M, and M 120000, we can equate:
3/4P 2/4 * 120000
3/4P 60000
P 60000 * 4/3
P 80000
Method 2
Representing the problem with symbols:
P Peter’s salary
M Mary’s salary 120000
3/4P 2/4M
3/4P 60000
P 60000 * 4/3
P 80000
Conclusion
In conclusion, by using the principles of proportion and algebra, we have found that Peter’s salary is 80000. This method not only helps in solving the given problem but also has broader applications in financial and economic contexts.