linear equation

Question

there were 268 tickets sold for a basketball game. The activity cardholders tickets cost $1.50 and the non cardholders tickets cost $2.25. The total amount of money collected was $536.25. How many of each kind of ticket were sold?

Answer 1

Let x = number of cardholders and let y = number of non-cardholders. We can set up a system of equations to model this situation:

 

x + y = 268        (268 total tickets sold)

1.5x + 2.25y = 536.25        (price cardholders paid plus price non-cardholders paid was $536.25)

 

 

Solve the first equation for x, then plug that into the second equation to solve for y:

 

x = 268 - y

 

1.5x + 2.25y = 536.25

1.5(268 - y) + 2.25y = 536.25

402 - 1.5y + 2.25y = 536.25

402 + 0.75y = 536.25

0.75y = 134.25

y = 179

 

 

There were y = 179 non-cardholder tickets sold. Plug that back into the first equation to solve for x:

 

x + y = 268

x + 179 = 268

x = 89

 

There were x = 89 cardholder tickets sold.