x = number of hot dogs sold

y = number of hamburgers sold

x + y = 213

2.5x = price per hot dog

3y = price per hamburger

2.5x + 3y = 575.5

Two equations in two unknowns

from first equation y = 213 -x

substitute that value for y in second equation;

2.5x + 3(213-x) = 575.5

solve for x to get number of hot dogs

subtract that amount from 213 to get the number of hamburgers