Question

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?

Answer 1

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.

Answer 2

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.