A train has a capacity of 154 seats. Tickets for seats are sold at $8 and
512. There are 1/5 more $8-seats than SI2-seats on the train. During a trip the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets. The total amount collected was $540. How
many $8-seats were not taken during the trip?
A train has a capacity of 154 seats. Tickets for seats are sold at $8 and
512. There are 1/5 more $8-seats than $12-seats on the train. During a trip the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets. The total amount collected was $540. How
many $8-seats were not taken during the trip?
Let x be the number of $12-seats on the train. Then the number of $8-seats on the train is 1/5 more than x, or (6/5)x.
The total number of seats on the train is:
x + (6/5)x = (11/5)x
Since the capacity of the train is 154 seats, we have:
(11/5)x = 154
x = 70
So there are 70 $12-seats and (6/5)(70) = 84 $8-seats on the train.
Let's use the variable y to represent the number of $8 tickets sold. Then the number of $12 tickets sold is 154 - y.
We know that the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets, so we can write:
8y = 2(12(154 - y))
Simplifying this equation, we get:
8y = 7392 - 24y
32y = 7392
y = 231
So 231 $8 tickets were sold and 154 - 231 = -77 $12 tickets were sold. Of course, we can't have a negative number of tickets sold, so we know that all of the $12-seats were empty and all of the $8-seats were filled.
Therefore, the number of $8-seats that were not taken during the trip is:
84 - 231 = -147
Again, we can't have a negative number of seats not taken, so we know that all 231 $8-seats were taken and none were left empty.
Therefore, the answer is that 0 $8-seats were not taken during the trip.
A train has a capacity of 154 seats. Tickets for seats are sold at $8 and
$12. There are 1/5 more $8-seats than $12-seats on the train. During a trip the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets. The total amount collected was $540. How
many $8-seats were not taken during the trip?
Let's call the number of $12-seats on the train "x". Then, since there are 1/5 more $8-seats than $12-seats, there are (6/5)x $8-seats on the train.
The total number of seats on the train is then:
x + (6/5)x = (11/5)x
We know that the capacity of the train is 154 seats, so:
(11/5)x = 154
x = 70
So there are 70 $12-seats and (6/5)(70) = 84 $8-seats on the train.
Let's represent the number of $8 tickets sold as "y". Then, we know that the number of $12 tickets sold is (154 - y).
We also know that the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets:
8y = 2(12(154 - y))
8y = 3696 - 24y
32y = 3696
y = 115.5
Since we can't sell a half ticket, we'll round down to 115 $8 tickets sold and 39 $12 tickets sold.
The total amount collected is:
(115 * 8) + (39 * 12) = $540
So, all the $12-seats were taken and there were 84 - 115 = -31 $8-seats not taken during the trip.
However, we can't have negative seats, so this means that all the $8-seats were actually taken and none were left empty.
Therefore, the answer is that 0 $8-seats were not taken during the trip.