Question

Two student groups from Gates Middle School went to a

Math Museum on the same day.
Group 1 bought 14 tickets and received a $75 discount.
Group 2 bought 10 tickets and received a $25 discount.
Both groups spent the same total of money on tickets.
The price of each ticket was the same.
What was the cost of each ticket?

Answer 1

To find the cost of each ticket, we can set up a system of equations based on the given information. Let's denote the cost of each ticket as "x".

For Group 1, they bought 14 tickets and received a $75 discount. So, the total amount spent by Group 1 can be expressed as:

14x - 75

For Group 2, they bought 10 tickets and received a $25 discount. So, the total amount spent by Group 2 can be expressed as:

10x - 25

According to the given information, both groups spent the same total amount on tickets. Therefore, we can set up an equation:

14x - 75 = 10x - 25

Simplifying this equation, we get:

4x = 50

Dividing both sides by 4, we find:

x = 12.5

Hence, the cost of each ticket is $12.50.

Explanation: