Question

Tickets to the school play are $10 for adults, $4 for students and $3 for senior citizens. There were 670 tickets sold for Thursday's show, worth $5615. If there were 65 tickets sold to senior citizens, how many tickets were sold to adults and how many were sold to students?​

Answer 1

500

105

Explanation:

This question would be solved using a simultaneous equation

let

a = number of adults who bought the ticket

b = number of students who bought the ticket

c = number of senior citizens who bought the ticket

a + b + c = 670 eqn 1

10a + 4b + 3c = 5615 -- eqn 2

If 65 senior citizen bought the ticket, substitute for c in equation 1 and 2

a + b + 65 = 670

a + b = 670 - 65

a + b = 605 eqn 3

10a + 4b + 3(65) = 5615

10a +4b = 5420 eqn 4

multiply equation 3 by 10 to derive equation 5. Subtract eqn 4 from eqn 5

10a + 10b = 6050 eqn 5

-

10a + 4b = 5420 eqn 4

= 6b = 630

b = 105

Students who bought the ticket are 105

Substitute for b in eqn 3

a + 105 = 605

a = 500

Adults who bought the ticket are 500