At a basketball game adult tickets were sold at 7.50 each and student tickets at 3.50 each if 205 were sold and 1317.50 was collected how many tickets if each kind were sold?

Answer 1

The formula to determine the total money is

nA + mC = 1317.50

where n is the number of adult tickets sold and A is the price of the adult tickets and m OS the number of child tickets and C is the price of a child ticket.

Substituting in the actual prices we get...

eq 1. n*7.50 + m * 3.50 = 1317.50

eq 2. n+m = 205

rearranging eq 2 we get

n = 205 - m

substituting this into eq 1 we get..

(205 -m) * 7.5 + m * 3.5 = 1317.50

Simplifying we get

1537.5 - 7.5m + 3.5m = 1317.50

1537.5 - 1317.5 = 4m

220 = 4m

55 = m

substituting into eqn 2 we get

n + 55 = 205

n = 150.

Therefor

150 Adult tickets were sold

55 Child tickets were sold