A restaurant 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