575 tickets were sold for a game for a total of $675.00. If adult tickets sold for $1.50 and children's tickets sold for $1.00, how many of each kind of ticket were sold?

Adult tickets sold: 200

Children's tickets sold: 375

Step-by-step explanation:

Set up equations

1.5x + 1y = 675

We got this equation because if we multiply the cost of the adult ticket with how many were sold, we get the total cost for adults. Since we don't know how many adult tickets were sold, we use x to represent that unknown value. $1.50x -> 1.5x

Same logic for the children's ticket, but since the amount of adult tickets and children's tickets may not be the same, we use a different variable, and in my example I will use y. $1y. We can simplify this to y.

If we add 1.5x to y, we should get the total cost, which is $675, so one of our equations looks like

1.5x + y = 675

For our next equation, we have:

x + y = 575

if x is the amount of adult tickets and y is the amount of children's tickets, the sum of these should be 575, as given by the problem.

Subtract

x + y = 575

from

1.5x + y = 675

1.5x + y = 675

x + y =575

1.5x-x= 0.5x y-y=0 675-575=100

0.5x + 0 = 100

0.5x = 100

x=200

Now that we have the amount of adult tickets (200, plug this into either of our earlier equations.

x + y = 575 would be easier to plug into

200 + y = 575

y = 375

So the amount of adult tickets sold is 200 and the amount of children's tickets sold is 375.

step-by-step explanation: examine the two-step equation.

−  

7

4

+  

x

4

= 2

which property of operations allows you to add the same constant term to both sides?

multiplication property of equality

division property of equality

addition property of equality

subtraction property of equality

14

step-by-step explanation: