A movie theater charges $7 for an adults ticket and $4 for a child's ticket. On a recent night the sale of child's ticket was three times the sale of adults tickets. If the total amount was not more than 2000 what is the greatest number of adults who could have purchased tickets

The greatest number of adults who could have purchased tickets is 105.

Step-by-step explanation:

Let the number of amount of adult tickets sold out be x

Therefore,

the number of amount of child tickets sold out be 3 * x

Total amount earned = 7 * x + 4 * 3 * x

= 19 * x

According to the question,

19 * x ≤ 2000

⇒ x ≤ 105

Hence,

The greatest number of adults who could have purchased tickets is 105.