Math Word Problem Help Please!?

Question

I am unsure how to find out how many activity cardholders' tickets were sold. Here is the question.

There were 226 tickets sold for a basketball game. The activity cardholder's tickets cost $1.75 and the non cardholder's tickets cost $2.25. The total amount collected was $425.50. How many activity cardholders' tickets were sold?

Thank you to anyone who answers this and could you possibly tell me the steps you took to get your answer, it would be most appreciative. :)

Answer 1

Here N represents non card holder'sticket, C represents cardholders ticket.

N+C = 226 --------- (1)

2.25N+1.75C = 425.50

Multiply by100 to each side in above equation.

225N+175C = 42550 --------- (2)

To eliminate the C value multiply (1) by 175

175N+175C = 39550 ----------(3)

Subtract (2) from (3)

225N+175C = 42550

175N+175C = 39550

(-)     (-)         (-)

_________________

50N = 3000

N = 3000/50

N = 60

Substitute the N value in (1)

60+C = 226

C = 226-60

C = 166

166 carholder's tickets were sold.

Check:

2.25N+1.75C = 425.50

2.25*60+1.75*166 =425.50

135+290.50 = 425.50

425.50 = 425.50