At the city museum, child admission is $5.20 and adult admission is $8.80. On Saturday, 119 tickets were sold for a total sales of $860.00 . How many adult tickets were sold that day?

## Algebra 2a, 10 Points For Correct Answer!?

March 19th, 2013 admin

adult tickets 67

child tickets 52

5.2x + 8.8y = 860

x + y = 119

Using Cramer’s rule we get x = 52 and y = 67, therefore 67 adult tickets were sold.

If all the tickets were children tickets, then the profit would be 119×5.2= $618.80

That is obviously not enough.

860 – 618.8 = 241.2

So we need to make 241.2 more than we are right now.

8.80 – 5.20 = 3.6

So for each adult ticket, you get 3.60 more than you would get from a child ticket.

So divide the needed money by 3.6

241.2/3.6=67

So there were 67 adult tickets.

Hope that makes sense!

Let X be the number of child tickets sold.

Let Y be the number of adult tickets sold

You know that 119 tickets were sold, so the number of child tickets + the number of adult tickets must be equal to 119.

Therefore X + Y = 119

And you know $860.00 were made.

So the money made from the amount of child tickets( $5.20 x X) + the money made from adult tickets ($8.80 x Y) must be equal to $860.00

So you have these too equations

X+Y = 119

and 5.2X + 8.8Y = 860

You then can use simultaneous equations to solve them