a.) Let x be the number of swimming lessons she had, then
402 - 15x = 237
b.) 15x = 402 - 237 = 165
x = 165/15 = 11
She had 11 swimming lessons
c.) Let the number of lesson she had be y, then 19y = 237
y = 237/19 = 12 lessons
She can pay for 12 lessons with her remaining $237.