In 10 minutes, the top three finishers in a hot dog eating contest consumed a total of 130 hot dogs. the winner, person a, ate 8 more hot dogs than the runner-up, person b. person c finished a distant third, 10 hot dogs behind person b. how many hot dogs did each person eat?

Let x be how many hot dogs person b ate

therefore, person a ate x+8 hotdogs
and person c ate x-10 hotdogs

they all ate 130 hotdogs in total so
x + x + 8 + x - 10 = 130
3x -2 = 130
3x = 132
x = 44

so person b ate 44 hotdogs
person a ate 8 more so 52 hotdogs
and person c ate 10 less than person b so 34 hotdogs