The movie theater sells a total of 100 tickets and makes a total of $880. if the theater charges $6 per child’s ticket and $10 per adult’s ticket. how many of each type of ticket did they sell?

They sell children’s 30 tickets and  70 adult’s tickets.

Explanation:

Let the number of child’s tickets=x

Number of adult’s tickets sold=y

Charge of child’s ticket=$6

Total number of tickets sold=100

Charge of adult’s ticket=$10

Total money made by selling tickets=$880

We have to represent the following situations in the form of two equations

Considering the number of tickets sold, we get the equation

x+y=100  

considering the  total money made by selling tickets

we get the equation 6x+10y=880  

we can solve this set of linear equations using

elimination method

x+y=100 (1)

6x+10y=880(2)

(1)*6

6x+6y=600 (3)

6x+10y=880(4)

(4)-(3)

6x+10y-6x-6y=880-600  

4y=280  

y=280/4=70  

substitute the value of in (1)  

x+70=100  

x=30