Question

The members of the city cultural center have decided to put on a play once a night for a

Answer 1

To answer the first question, we have these two equations:

x + y = 500 and 7.5x + 4.5y = 2550

We can use substitution to solve for x and then plug it back into any equation and find y.

y = 500 - x

7.5x + 4.5 (500 - x) = 2550

7.5x + 2250 - 4.5x = 2550

3x = 300

x = 100 adults

100 + y = 500 → y = 400 students

To answer your second question, we have two new equations:

2x = y (This may be confusing, but since there were more student tickets sold, it is the larger number.)
x + y = 300

We can rewrite the first equation and add them together:

2x - y = 0
x + y = 300

3x = 300

x = 100 adults

100 + y = 300 y = 200 students

The money earned from these 300 people is 100 * 7.5 + 200 * 4.5 = 750 + 900 = $1650.

$2550 - $1650 = $900

The 300 tickets sold had a $900 fall in ticket sales.

Hope this helps!