There were 300 people at a dance. tickets cost $5 for visitors and $3 for students. the total tickets sales were $1100. how many visitors and how many students attended the dance?

Given:

Number of people = 300

Ticket cost for visitors = $5 and for students = $3

Total ticket sales = $1100

To find: Number of visitors and number of students.

Solution:

Let number of students be x and number of visitors be y.

By above information, we get 2 equations,

1. x + y = 300

2. 3x + 5y = 1100

Now, balancing the equations, multiply equation 1. with 3 and equation 2. with 1

Now we get 3x + 3y = 900 - equation 3

and 3x + 5y = 1100 - equation 4

By subtracting equation 4 from equation 3, we get

-2y = - 200

By solving this we get y = 100

Putting value of y = 100 in equation 1.

x+100 = 300

x = 200

So, number of students = 200 and number of visitors = 100.

X-visitor

y-student

Total amount of people: x+y=300

The total tickets sales: $5*x+$3*y=$1100

x+y=300⇒x=300-y

5x+3y=1100

x=300-y

5 * (300-y) + 3y=1100⇒1500-5y+3y=1100⇒2y=400⇒y=200

x=300-200=100

100 visitors and 200 students attended the dance.