Question

4 a standard ticket for the neesing metro system costs $10 and is valid for unlimited travel on the system for the whole of the day it is bought. also available are a 3 - day ticket for $15 and a 7 - day ticket for $30. these tickets are valid for 3 or 7 consecutive days respectively, starting from the day of purchase. this table shows the number of tickets sold during the first two weeks of last month. date standard tickets 3 - day tickets 7 - day tickets 1st 523 288 173 2nd 641 307 158 3rd 506 345 212 4th 593 382 191 5th 674 311 170 6th 549 326 183 7th 729 355 192 8th 763 394 218 9th 602 337 189 10th 518 256 170 11th 675 325 196 12th 549 360 183 13th 510 264 162 14th 734 343 205 (a) explain how it can be deduced, without calculation, that the total income from ticket sales was greater on the 8th than on any other day during the first two weeks of last month. 1

Explanation:

On the 8th, the number of each type of ticket sold (standard, 3-day, 7-day) is higher than or equal to the number sold on every other single day. Since each ticket type has a fixed positive price, higher quantities sold for all ticket categories mean the total income will be the highest on this day.

Answer:

The 8th has the highest number of every ticket type sold among all 14 days; since each ticket has a positive cost, this guarantees the highest total income for that day.