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Question

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?

All work must be shown in order to get credit...thanks.

Answer 1

We will be happy to critique your work.

Answer 2

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