Petra is a designer in the fashion industry. She designs 2 pairs of shoes for every 5 dresses. Mary is a design student and plans to spend the summer as Petra's intern. She knows that Petra has designed a total of 115 dresses, but she wants to know how many pairs of shoes she has designed. To figure this out, Mary decides to use a proportion.

To solve the problem, Mary set up the following proportion and solved for the number of pairs of shoes Petra designed as shown below.

Based on the proportion, there is some number d that when multiplied by 5 will give 115. Since the proportion will stay the same when the numerator and denominator are multiplied by the same thing, Mary rewrites the proportion as follows.

This leads to two equations, 2d = x and 5d = 115.

By solving the equation 5d = 115, d = 23. Using this, 2d = 2(23) = 46 = x.

So, Mary determines that Petra designed 46 pairs of shoes.

Part A: Describe another method for solving a proportion.

Part B: Use the method that is described in Part A to solve the proportion and explain any differences in the final result.