Question

Jin sells concert tickets at the theater box office. The ratio of student tickets to adult tickets sold is 4 : 5. Each student ticket costs $5, and each adult ticket costs $7. Jin sells 189 tickets altogether. Part A: How many student tickets does Jin sell? How many adult tickets? Explain your reasoning. Part B: How much more money does Jin receive from selling adult tickets than from selling student tickets? Explain your reasoning​

Answer 1

Explanation:

1) if total number of the saled tickets is 189, then it is possible to write s+a=189, where s - number of student tickets, a - adult tickets.
2) if the ratio is 4:5, then it is possible to write s:a=4:5;

3) using the two equations it is possible to make up the system:

`\left \{ {{s+a=189} \atop {(s)/(a) =(4)/(5) }} \right.`

4) Part A: after solution the system above the number of student tickets = 84; adult tickets = 105.

5) Part B: the revenue from selling the adult tickets is: 105*7=735, the student tickets is: 84*5=420. Then the required difference is: 735-420=$ 315.