Let x represent the number of pounds of Swiss cheese that Marsha bought.
We were told that Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. This means that the cost of 3 pounds of cheddar cheese is 3 * 4.50 = 13.5
Also, the cost of x pounds of Swiss cheese is 4.5 * x = 4.5x
If the total cost is $24.75, it means that
4.5x + 13.5 = 24.75
The equation is
4.5x + 13.5 = 24.75
We would solve for x. Thus,
4.5x = 24.75 - 13.5
4.5x = 11.25
x = 11.25/4.5
x = 2.5
Thus, she bought 2.5 pounds of Swiss cheese