Question 1197109
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Start with this: the total number of tickets is 360, and the number of general admission tickets was 40 more than the rest.<br>
Use formal algebra if you want; or use logical reasoning and simple arithmetic to determine that 200 of the 360 tickets were general admission.<br>
Those 200 general admission tickets cost a total of 200($5) = $1000, meaning the other 160 tickets cost a total of $2800-$1000 = $1800.<br>
You can then use formal algebra to set up a pair of equations to find the numbers of VIP seating tickets and reserved seating tickets -- something like<br>
x+y = 160  (total number of tickets)
15x+10y=1800  (total cost of the tickets)<br>
That system of equations is easily solved by any of several standard algebraic techniques.<br>
But this remaining part of the problem can also be solved using logical reasoning and simple arithmetic, as follows.<br>
(1) If all 160 remaining tickets were reserved seating tickets, their total cost would have been $1600
(2) But the actual cost is $1800, which is $200 more
(3) Each VIP seating ticket costs $5 more than each reserved seating ticket
(4) To make the additional $200, the number of VIP seating tickets had to be 200/5 = 40<br>
So of the remaining 160 tickets, 40 were VIP seating tickets, meaning 120 were reserved seating tickets.<br>
ANSWER:
VIP seating: 40
reserved seating: 120
general admission: 200<br>
CHECK: 40(15)+120(10)+200(5) = 600+1200+1000 = 2800<br>