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In a movie theater, Theater A has 30 seats in the first row. Each 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?

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 row, how many more seats does Theater B have in it than Theater A?

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1)

Numbers of seats in rows in Theater A:

RA=FA+(n-1)*4

FA=Numbers of seats in first row=30

n-number of row

RA=30+(n-1)*4

first row has 30 seats

second row has:
30+(2-1)*4=30+1*4=30+4=34 seats

third row has:
30+(3-1)*4= 30+2*4=30+8=38 seats

fourth row has:
30+(4-1)*4=30+3*4=30+12=42 seats

2)
Numbers of seats in rows in Theater A:

RA=FA+(n-1)*4

FA=Numbers of seats in first row=30

n-number of row

RA=30+(n-1)*4

first row has 30 seats

second row has:
30+(2-1)*4=30+1*4=30+4=34 seats

third row has:
30+(3-1)*4= 30+2*4=30+8=38 seats

fourth row has:
30+(4-1)*4=30+3*4=30+12=42 seats

fifth row has:
30+(5-1)*4=30+4*4=30+16=46 seats

sixth row has:
30+(6-1)*4=30+5*4=30+20=50 seats

seventh row has:
30+(7-1)*4=30+6*4=30+24=54 seats

eighth row has:
30+(8-1)*4=30+7*4=30+28=58 seats

ninth row has:
30+(9-1)*4=30+8*4=30+32=62 seats

tenth row has:
30+(10-1)*4=30+9*4=30+36=66 seats

Is there a row with exactly 60 seats in it? NO

3)

In Teater B first row has 40 seats,and each row has 4 more seats in it than the previous row has.

In Teater B first row has 30 seats,and each row has 4 more seats in it than the previous row has.

40-30=10

That means that each row in theatre B has 10 seats more then row in Theatre A.

If both Theaters has 25 rows.

Difference between numbers of seats in Theater A and Theater B is:

25*10=250 seats

To answer these questions, we need to understand the pattern of seat increase in each row in Theater A and Theater B.

For Theater A:
The first row has 30 seats.
Each row has 4 more seats than the previous row.

1) To find the number of seats in the 4th row of Theater A, we start with the number of seats in the first row and add 4 seats for each subsequent row. So:
Number of seats in the 4th row = Number of seats in the first row + (Number of rows - 1) * 4

Since the first row has 30 seats and we need to find the 4th row, we can substitute the values:
Number of seats in the 4th row = 30 + (4 - 1) * 4
Number of seats in the 4th row = 30 + 3 * 4
Number of seats in the 4th row = 30 + 12
Number of seats in the 4th row = 42

Therefore, the 4th row in Theater A has 42 seats.

2) To check if there is a row with exactly 60 seats in it in Theater A, we need to find if any row has 60 seats using the same pattern.

Number of seats in a row = Number of seats in the first row + (Number of rows - 1) * 4

Let's check by substituting the values:
Number of seats in a row = 30 + (n - 1) * 4, where n is the row number.

To find if there's a row with exactly 60 seats, we can use the equation:
60 = 30 + (n - 1) * 4

Now we will solve this equation:
30 + (n - 1) * 4 = 60
(n - 1) * 4 = 60 - 30
(n - 1) * 4 = 30
n - 1 = 30 / 4
n - 1 = 7.5
n = 7.5 + 1
n = 8.5

Since row numbers are usually whole numbers, there is no row in Theater A with exactly 60 seats.

Now let's move on to Theater B:

For Theater B:
The first row has 40 seats.
Each row has 4 more seats than the previous row.

3) To find out how many more seats Theater B has than Theater A, we need to calculate the total number of seats in both theaters.

Number of seats in Theater A = (Number of seats in the first row + Number of seats in the last row) * Number of rows / 2
Number of seats in Theater A = (30 + (30 + (Number of rows - 1) * 4)) * Number of rows / 2
Number of seats in Theater A = (60 + (Number of rows - 1) * 4) * Number of rows / 2

Number of seats in Theater B = (Number of seats in the first row + (Number of seats in the first row + (Number of rows - 1) * 4)) * Number of rows / 2
Number of seats in Theater B = (40 + (40 + (Number of rows - 1) * 4)) * Number of rows / 2
Number of seats in Theater B = (80 + (Number of rows - 1) * 4) * Number of rows / 2

We can now calculate the difference between the total number of seats in Theater B and Theater A:

Difference = Number of seats in Theater B - Number of seats in Theater A
Difference = [(80 + (Number of rows - 1) * 4) * Number of rows / 2] - [(60 + (Number of rows - 1) * 4) * Number of rows / 2]
Difference = [80 + (Number of rows - 1) * 4 - 60] * Number of rows / 2
Difference = (20 + (Number of rows - 1) * 4) * Number of rows / 2
Difference = (20 + 4 * Number of rows - 4) * Number of rows / 2
Difference = (16 + 4 * Number of rows) * Number of rows / 2
Difference = 2 * (8 + Number of rows) * Number of rows / 2
Difference = (8 + Number of rows) * Number of rows

To find the difference, we need to know the number of rows. Since it is not mentioned in the question, we cannot calculate the exact difference. But we have the equation, so we can substitute the value of the number of rows into the equation to find the difference.

Remember to show all the steps and calculations to get credit for the answer.