tickets to a concert cost $15 online and $25 at the door. One hundred more people bought their tickets at the door than online and if the total ticket sales were $20,500, how many more people bought their tickets online
Answers
Tickets to a concert cost $15 online and $25 at the door. One hundred more people bought their tickets at the door than online and if the total ticket sales were $20,500, how many more people bought their tickets online ?
We can come up with two applicable equations from the information given.
eqn 1) A + D = 120 total number of tickets sold
eqn 2) 10A + 15D = 1380.90 total amount of money made
at $10 for advance tickets
and $15 for door bought tickets
We can use two different methods to solve this system. Elimination or
substitution. Your instructions state to solve by substitution.
Note: I can already see that there is a problem. Your ticket prices are
both in whole dollar amounts - no change. But, they brought in
$1380.90... That means the number of tickets sold of each type isn't
going to come out in whole numbers.... Still, let's work the problem.
From equation 1, subtract A from both sides giving:
D = 120 - A
Substitute 120-A in place of D in equation 2 and solve for A.
10A + 15(120-A) = 1380.9 multiply through the parenthesis
10A + 15(120) + 15(-A) = 1380.9
10A + 1800 -15A = 1380.9 combine like terms
-5A + 1800 = 1380.9 subtract 1800 from both sides
-5A = 1380.9 - 1800
-5A = -419.1 divide both sides by -5
A = 83.82
As I said, this didn't come out in a whole number. Your problem
is either written incorrectly, or is missing some information.
Maybe there was a tax applied...
With the information as given, I would round A to 84