The admission ticket to a baseball game is $\$5$ for children and $\$9$ for adults. On a certain night, 900 people were present at the baseball game and $\$6,500$ was collected. How many people attended the baseball game?
Part A.) Write a system of equations to represent this situation.
Part B.) Solve the system algebraically to find out how many children attended the baseball game.
We can write this as a system of equations. Let c be the number of children and a be the number of adults who attended.
900 people were present at the game ==> a + c = 900 . (1)
$6500 was collected ==> 9a + 5c = 6500 . (2)
We can use the elimination method to find a and c. Multiply equation (1) by 5:
5a + 5c = 4500
9a + 5c = 6500
Subtracting both equations yields -4a = -2000, so a = 500 and c = 400.
Apologies for the formatting, I am new to the site.