There were 654 tickets sold for a basketball game. The activity cardholders' tickets cost 1.5 and the non-cardholders' tickets cost 2.00. the total amount of money collected was 1171.50. how many of each kind of tickets were sold.

x = activity cardholders

y = non-cardhoolders

x + y = 654 tickets
1.50x + 2.00y = 1171.50

x = 654 - y

1.50(654-y) + 2.00y = 1171.50
981 - 1.50y + 2.00y = 1171.50
981 + .50y = 1171.50
.50y = 190.5
y = 381

x + 381 = 654
x = 273

273 activity cardholders
381 non-cardholders

273(1.50) + 381(2.00) = 1171.50
409.50 + 762 = 1171.50
1171.5 = 1171.50

To solve this problem, we can set up a system of equations based on the given information.

Let's assume the number of activity cardholders' tickets sold is "x," and the number of non-cardholders' tickets sold is "y."

Based on the given information, we can set up the following equations:

1) x + y = 654 (since the total number of tickets sold was 654)
2) 1.5x + 2y = 1171.50 (since the total amount of money collected was 1171.50)

To simplify the calculations, let's multiply the second equation by 2 to eliminate decimals, making it:

3x + 4y = 2343

Now, we have two equations:

1) x + y = 654
2) 3x + 4y = 2343

You can solve this system of equations by either substitution or elimination.

Using substitution:
From equation 1), we can isolate x as x = 654 - y
Substituting this value for x in equation 2), we get:
3(654 - y) + 4y = 2343
1962 - 3y + 4y = 2343
y = 381

Now that we have the value of y, we can substitute it back into equation 1) or x = 654 - y:
x = 654 - 381
x = 273

Therefore, there were 273 activity cardholders' tickets sold and 381 non-cardholders' tickets sold.