let

c = the number of card holders tickets

n = the number of non cardholders tickets

there were 523 tickets sold for the basketball game

c + n = 532

the activity card holders tickets cost $1.75 and the non cardholders cost $2.50. the amount of money collected was $1139.50.

1.75c + 2.50n = 1139.50

by solving the system of equations

c + n = 532

1.75c + 2.50n = 1139.50

we find

c = 254 card holders tickets

n = 278 non-card holders tickets

click here to see the step by step solution of the system of equations

there were 254 card holders tickets and 278 non-card holders tickets sold.