Two student groups went to an amusement park on the same day.

Question

Two student groups went to an amusement park on the same day.

Group 1 bought 9 tickets and received a $120 discount.
Group 2 bought 3 tickets and received a $30 discount.
Both groups spent the same total amount of money on tickets.
The price of each ticket was the same.
What was the cost of each ticket?

Question 9 options:

$25

$12.50

$15

$7.50

Answer 1

Let's assume that the cost of each ticket is "x".

For Group 1, the cost of 9 tickets without the discount would be 9x. Since they received a $120 discount, the total amount they spent on tickets is 9x - $120.

For Group 2, the cost of 3 tickets without the discount would be 3x. Since they received a $30 discount, the total amount they spent on tickets is 3x - $30.

Since both groups spent the same total amount of money on tickets, we can set up the following equation:

9x - $120 = 3x - $30

Simplifying the equation, we get:

6x = $90

Dividing both sides by 6, we get:

x = $15

Therefore, the cost of each ticket is $15. Answer: $\boxed{15}$.

Answer 2

To find the cost of each ticket, we need to determine the total amount spent by each group.

Let's assume the cost of each ticket is "x" dollars.

For Group 1:
Number of tickets = 9
Discount received = $120
Total amount spent = (Number of tickets * Cost of each ticket) - Discount
= (9 * x) - $120

For Group 2:
Number of tickets = 3
Discount received = $30
Total amount spent = (Number of tickets * Cost of each ticket) - Discount
= (3 * x) - $30

Since both groups spent the same total amount on tickets:
(9 * x) - $120 = (3 * x) - $30

Simplifying the equation:
9x - 120 = 3x - 30

Bringing the "x" terms to one side:
9x - 3x = -30 + 120
6x = 90

Dividing by 6:
x = 90 / 6
x = 15

Therefore, the cost of each ticket is $15.

So, the correct answer is Option C) $15.

Answer 3

To find the cost of each ticket, let's set up equations for both groups:

Let's assume the cost of each ticket is x dollars.

For Group 1:
Total cost of tickets = Number of tickets × Cost per ticket
9x = Total cost of tickets for Group 1

For Group 2:
Total cost of tickets = Number of tickets × Cost per ticket
3x = Total cost of tickets for Group 2

We are given that both groups spent the same total amount of money on tickets, so we can set up an equation based on that:
Total cost of tickets for Group 1 = Total cost of tickets for Group 2

9x = 3x

To find x, let's subtract 3x from both sides of the equation:
9x - 3x = 0
6x = 0

Divide both sides of the equation by 6 to solve for x:
x = 0 / 6
x = 0

Oops! It seems we made an error in the calculation. Let's go back and try again:

9x - 120 = 3x - 30

Let's subtract 3x from both sides of the equation:
9x - 3x - 120 = 3x - 3x - 30
6x - 120 = -30

Next, let's add 120 to both sides of the equation:
6x - 120 + 120 = -30 + 120
6x = 90

Finally, let's divide both sides of the equation by 6 to solve for x:
x = 90 / 6
x = $15

Therefore, the cost of each ticket is $15.

The correct answer is $15.