Question

6. Кассир кинотеатра записал количество проданных билетов на один и тот же фильм за четыре дня подряд, и заметил, что число проданных билетов образует закономерную последовательность: 154; 148; 136; 112; … Сколько билетов будет продано в пятый день?

Answer 1

Ответ:

на пятый день было продано 64 билетов

Пошаговое объяснение:

154-148=6

154-6=148

6*2=12

148-12=136

12*2=24

136-24=112

24*2=48

112-48=64

Answer 2

154. 148. 136. 112. 62.

Answer 3

Problem Analysis

The cashier at a movie theater has recorded the number of tickets sold for the same movie over four consecutive days and noticed that the number of tickets sold forms a regular sequence: 154, 148, 136, 112. The task is to determine how many tickets will be sold on the fifth day.

Solution

To find the pattern in the sequence of ticket sales, we can calculate the differences between consecutive terms:

| Day | Number of Tickets Sold | |-----|-----------------------| | 1 | 154 | | 2 | 148 | | 3 | 136 | | 4 | 112 |

The differences between consecutive terms are:

| Day Difference | Difference in Tickets Sold | |----------------|---------------------------| | 1-2 | 6 | | 2-3 | 12 | | 3-4 | 24 |

We can observe that the differences form a geometric sequence with a common ratio of 2. This means that each day, the number of tickets sold decreases by a factor of 2.

To find the number of tickets sold on the fifth day, we can continue the pattern:

| Day | Number of Tickets Sold | |-----|-----------------------| | 1 | 154 | | 2 | 148 | | 3 | 136 | | 4 | 112 | | 5 | ? |

Starting from the fourth day, we can calculate the number of tickets sold on the fifth day by multiplying the number of tickets sold on the fourth day by the common ratio of 2:

Number of tickets sold on the fifth day = Number of tickets sold on the fourth day * Common ratio

Let's calculate it:

Number of tickets sold on the fifth day = 112 * 2 = 224.

Therefore, the cashier will sell 224 tickets on the fifth day.

Conclusion

The cashier at the movie theater will sell 224 tickets on the fifth day, based on the observed pattern of ticket sales over the previous four days.