<u>Note: The only way to solve this problem is by adjusting the fees to $3.50 and $7.50.</u>
Answer:
<em>1300 children attended the basketball game</em>
Step-by-step explanation:
System of Equations
Let's call:
x = number of children attending the basketball game
y = number of adults attending the basketball game
On a certain night, 1500 people enter the game, thus:
x + y = 1500 [1]
Since each admission fee for children cost $3.50 and $7.50 for adults and it was collected $6050, thus:
3.50x + 7.50y = 6050 [2]
From [1]:
y = 1500 - x
Substituting in [2]:
3.50x + 7.50(1500 - x) = 6050
Operating:
3.50x + 11250 - 7.50 = 6050
-4x = 6050 - 11250
Solving:
x = 1300
1300 children attended the basketball game
If A and B are independent, then 
.
a.
b. I'm guessing the ? is supposed to stand for intersection. We can use DeMorgan's law for complements here:
c. DeMorgan's law can be used here too:
2x-3+7x-10=32
9x-13=32
9x=32+13
9x=45
x=5
