What's the greatest number of adults who could've purchased tickets?

Question

A movie theater charges $7 for an adult's ticket and $4 for a child's ticket. On a recent night, the sale of child's tickets was 3 times the sale of adult's tickets. If the total amount collected for the ticket sales wasn't more than $2,000, what's the greatest number of adults who could've purchased tickets?

Answer 1

no.of adults purchased movie ticket = x

no. of children purchased movie ticket =y

 

the sale of child's tickets was 3 times the sale of adult's tickets: y= 3x

 

the total amount collected for the ticket sales wasn't more than $2,000 :

 

 

7x +4y<= 2000

 

7x +4(3x) <=2000

7x+12x<=2000

19x <=2000

 

x<= 105.26

 

the greatest number of adults who could've purchased tickets<=105