Ticket Sales and the Missing Notes
A school drama club sells tickets for two nights. Adult tickets cost $8, student tickets $5. On Friday, 143 tickets are sold and $922 is collected. On Saturday, 96 adult tickets and 71 student tickets are sold, but the treasurer's note says only "Saturday total collected: $1,108" and someone has crossed it out. The club president remembers that on Saturday a group of 12 students were charged the adult price by mistake. The club needs to report each night's totals separately and must decide whether the crossed-out figure is consistent with the corrected Saturday sales.
1. Find how many adult and student tickets were sold on Friday, and check whether the result is possible in whole tickets.
Read the worked answer
Let a = adult tickets and s = student tickets on Friday.
Equations:
- a + s = 143
- 8a + 5s = 922
From the first, s = 143 − a. Substitute: 8a + 5(143 − a) = 922 8a + 715 − 5a = 922 3a = 207 a = 69
Then s = 143 − 69 = 74.
Check: 8(69) + 5(74) = 552 + 370 = 922. ✓
Both values are whole numbers, so the Friday record is consistent.
2. Correct the Saturday sales and decide whether $1,108 could be the true corrected total.
Read the worked answer
Saturday recorded sales: 96 adult and 71 student, but 12 of the students were charged as adults.
Corrected counts:
- Adult tickets: 96 + 12 = 108
- Student tickets: 71 − 12 = 59
Corrected total: 8(108) + 5(59) = 864 + 295 = $1,159.
So $1,108 is not the corrected total. It is $51 too low. Note that the error direction matters: charging students as adults raises the total, so the crossed-out figure cannot be a corrected value below the corrected total of $1,159 unless other errors exist. The club should report $1,159 and investigate the $51 discrepancy separately.