In a movie theater, Theater A has 30 seats in the first row. Each next row has 4 more seats in it than the previous row has.
1) How many seats are in the 4th row?
2) Is there a row with exactly 60 seats in it? Explain.
3) Theater B has 40 seats in the first row and each row has 4 more seats than the previous row. If both Theater A and Theater B has 25 rows, how many more seats does Theater B have in it than theater A?
PLZ HELP---CANNOT FIGURE THIS OUT.
1) 30, 34, 38, 42
2) . . 46, 50, 54, 58, 62
You try number 3.
1) To find the number of seats in the 4th row of Theater A, we need to determine the pattern of seat increase. We know that the first row has 30 seats. Each subsequent row has 4 more seats than the previous row.
So, for the second row, we add 4 seats to 30, giving us 34 seats. For the third row, we add another 4 seats to 34, giving us 38 seats. Following the same pattern, we add 4 more seats to get the number of seats in the 4th row.
30 + 4 + 4 + 4 = 42
Therefore, there are 42 seats in the 4th row of Theater A.
2) To determine if there is a row with exactly 60 seats in Theater A, we need to observe the pattern of seat increase again. Since each row has 4 more seats than the previous row, we can determine if 60 seats is possible.
The first row has 30 seats, and each subsequent row has 4 more seats. If we continue this pattern, we can calculate the number of seats in the following rows:
- The second row has 34 seats
- The third row has 38 seats
- The fourth row has 42 seats
- The fifth row has 46 seats
As we can see, the number of seats in each row is increasing, but it will not reach 60 seats in any row. Therefore, there is no row with exactly 60 seats in Theater A.
3) To determine the difference in the number of seats between Theater A and Theater B, we need to consider the seat increase pattern for both theaters.
Theater A has 30 seats in the first row, and each subsequent row has 4 more seats. Therefore, the number of seats in each row can be calculated as follows:
Row 1: 30 seats
Row 2: 30 + 4 = 34 seats
Row 3: 34 + 4 = 38 seats
...and so on.
Theater B has 40 seats in the first row, and each subsequent row has 4 more seats. The number of seats in each row of Theater B can be calculated in a similar manner.
Since both Theater A and Theater B have 25 rows, we need to calculate the total number of seats in each theater and find the difference.
For Theater A:
Total seats = (30 + 34 + 38 + ...) for 25 rows
For Theater B:
Total seats = (40 + 44 + 48 + ...) for 25 rows
We need to find the difference between the total seats in Theater B and Theater A.
By calculating the sums for both theaters, we can compare the results to find the difference.