Question

At a lacrosse tournament, students are charged $7 per ticket and adults are charged $10 per ticket. If 450 people attended the tournament, and a total of $4,200 was collected in ticket fees, how many students attended the tournament?

Answer 1

100 students who attended the tournament.

Explanation:

Let's use algebra to solve the problem. Let's call the number of students who attended the tournament "s" and the number of adults who attended the tournament "a". Then we can write two equations based on the information given:

s + a = 450 (equation 1)

7s + 10a = 4200 (equation 2)

Equation 1 represents the total number of people who attended the tournament, which is 450. Equation 2 represents the total amount of money collected in ticket fees, which is $4,200.

To solve for "s", we can use elimination or substitution. Let's use elimination. We can multiply equation 1 by -7 to get:

-7s - 7a = -3150 (equation 3)

Now we can add equation 3 to equation 2:

-7s - 7a + 7s + 10a = -3150 + 4200

Simplifying the left side and solving for "a", we get:

3a = 1050

a = 350

So there were 350 adults who attended the tournament. We can substitute this value back into equation 1 to solve for "s":

s + 350 = 450

s = 100

Therefore, there were 100 students who attended the tournament.

Answer 2

100

Explanation:

How many students attended the tournament?

The simultaneous equations that would be used to solve this question is:

10a + 7s = 4,200 equation 1

a + s = 450 equation 2

Where:

a = number of adults

s = number of students

The elimination method would be used to solve the equations.

Multiply equation 2 by 10

10a + 10s = 4500 equation 3

3s = 300

Divide both sides of the equation by 3

s = 300 / 3

s = 100