At the movie theatre, child admission is 6.30 and adult admission is 9.40. on wednesday, 155 tickets were sold for a total sales of 1233.80. how many adult tickets were sold that day?

Define x and y:

Let x be the number of adult tickets sold.
Let y be the number of child tickets sold.


Construct equations:

There were 155 tickets sold
⇒ x+ y = 155

Total sales is $1233.80
⇒9.4x + 6.3y = 1233.8


Solve for x and y:

x + y = 155            (1)
9.4x + 6.3y = 1233.8 (2)


From equation 1:

x + y = 155
x = 155 - y


Sub x = 155 - y into equation 2:

9.4 (155 - y) + 6.3y = 1233.8
1457 - 9.4y + 6.3y = 1233.8 .   // Apply distributive property
1457 - 3.1y = 1233.8                // Combine like terms
1457 = 3.1y +1233.8                // Add 3.1y on both sides
233.2 = 3.1y                             // Subtract 1233.8 from both sides
72 = y                                       // Divide by 3.1 on both sides
y = 72                                       // Make y the subject


Sub y = 72 into equation 1:

x + y = 155
x + 72 = 155                           // Sub y = 72
x = 83                                     // Take away 72 from both sides


Find the number of adult and child tickets sold:

Adult = x = 83
Child = y= 72 


83 Adult tickets were sold that day.