Arestaurant manager wants to purchase 200200 sets of dishes. one design costs $1010 per set, while another costs $5555 per set. if she wants to use her entire budget of $78507850, how many of each design should be ordered?

Unless it was a restaurant for the king i am going to assume your 
200200 is 200
$1010 is $10
$5555 is $55
$78507850 is $7850 

Let x be the number of $10 design set
$10 design set = x
$55 design set = 200 - x

10x + 55(200 - x) = 7850
10x + 11000 - 55x = 7850
55x - 10x = 11000 - 7850
45x = 3150
x = 70
200 - 70 = 130

70 of the $10 design and 130 of the $55 design

You didn’t put the necessary image to solve the question : p