Y6 – 1/6 – Maths -Theatre trouble! Help!

Miss Vega want to open a new theatre in Coventry, but she is having issues with some of the measurements. Below are the basic measurements you will need to help solve the investigation. I am SO stuck – please help me year 6!!!

I would like everyone to try the first two questions at least... The more that you can complete the better – this is a challenge! There might even be a prize for the first person who completes (showing their working out) all of the questions correctly…

The theatre is 43m long and 27m wide.

The stage is as wide as the theatre and had a total area of 324 metres squared.

The orchestra pit is also as wide as the theatre and had a total area of 81 metres squared.

Miss Vega needs to know how many seats she can fit in the remaining space. Each seat is 50cm long and 50cm wide. There must also be 50cm of space between each row as legroom.

Because of fire safety regulations, there must be an aisle running down the middle of the theatre. This aisle is 3m wide. There must also be an aisle on each side. These are 1m wide.

Miss Amhed’s group – please complete this additions challenge (in blue) only

Miss Vega has the following expenses when putting on a performance:

ExpenseCost for each performance
Actor’s salaries£8321.17
Musician’s salaries£1437.85
Lighting£1652.79
Sound£1528.92
Costumes£3832.45
Theatre rent£1000.00
Publicity (posters, adverts etc.)£3326.73

What is the total of expenses for each performance? Add each of the amounts together…

Question 1: How many rows of seats can Miss Vega have in her theatre?

Question 2: How many seats can Miss Vega have in each row?

Question 3: How many seats can Miss Vega have in the whole theatre?

I plan to charge £30 per seat in the first 6 rows, £20 per seat in the next 6 rows and £10 per seat in all the other rows.

Question 4: How much money will Miss Vega make from each performance if the theatre is sold out?

Question 5: Does Miss Vega make a profit or a loss on each performance? How much does she gain/lose?

Good Luck! I cannot wait to see who is going to help me solve my issues quickest!

67 thoughts on “Y6 – 1/6 – Maths -Theatre trouble! Help!

  1. The area of the whole theatre is 1161meters squared
    The stage in width is 27 and the length is 12 because the are of it is 324 so you have divide to find length.
    The orchestra pit also in 27 meters so you but you already know the area is 81.It would 3 groups of 27 to make 81.So the length is 3 meters.
    You could fit at least 56 seats in a across and 14 seats down.
    In the whole theatre using the whole space and following the rules you could put a whopping 64 in a row and 21 seats down.

  2. 1) there are 28 rows.
    2) dhe can have 44 seats in a whole row.
    3) she can have 1232 seats in the entire theatre.
    4) miss vega would make £20240
    5) miss vega looses £859.91. Miss vega previously gained £20240.

  3. 1)Miss Vega can have 28 rows in her theatre.
    2)There are 44 seats in each row.
    3)There are 1232 seats in total.
    4)When tickets are sold out, Miss vega would make £348-£360.

  4. 1)Miss Vega has 28 rows of seats.
    2)There are 44 seats in each row.
    3)There will be 1232 seat in total.
    4)Miss Vega would get £460 from each solid performance.
    5)Miss Vega will lose £85891.
    Miss Vega gains £20140.

  5. 1. Miss Vega can have 24 rows of seats.
    2. Miss Vega can have 44 seats in each row.
    3. Miss Vega can have 1232 seats in the whole theatre.
    4. Miss Vega would gain £20,240 per theatre show.
    5. Miss Vega made a loss of £857.91. I know this because the cost of the show is 21,097.91 and she only gained £20,240 which makes her lose £857.91.

  6. !)The amount of rows of seats that there are, are 28.
    2)In each one of the rows, there will be 44 seats.
    3)1232 seats altogether.
    (She spends £21,099.87 on each performance.)
    4)Miss Vega will make:£460 by the time the tickets are sold out.
    5)She made a loss of:£857.91 as the show costed £21,097.91 but gained £20,240.

  7. 1. There are 28 rows of seats.
    2. There would be 44 seats in each row.
    3. There are 1,232 seats in the whole theatre.
    4. Miss Vega would gain £20,240 per theatre show.
    5. She has made a loss of £857.91 because the cost of the show is 21,097.91 and she only gained £20,240.

  8. Question 5: Does Miss Vega make a profit or a loss on each performance? How much does she gain/lose?I
    8321.17+1437.85+1652.79+1528.92+3832.45+1000.00+3326.73=
    £21099.91
    The expenses are more than the money she warned by each performance, therefore she is in a loss of £859.91

  9. Question 1: How many rows of seats can Miss Vega have in her theatre?
    Answer= 28 rows

    Question 2: How many seats can Miss Vega have in each row?
    11÷0.5 = 22, 22×2=44 seats in each row

    Question 3: How many seats can Miss Vega have in the whole theatre?
    44×28=1232 seats in the whole theatre

    I plan to charge £30 per seat in the first 6 rows, £20 per seat in the next 6 rows and £10 per seat in all the other rows.
    Question 4: How much money will Miss Vega make from each performance if the theatre is sold out?I

    total Seats in first six rows = 44×6= 264 seats
    264×30=£7920
    Seats in the next six rows = 44×6=264
    264×20=£5280
    Remaining rows are 28-12=16 rows
    16×44= 704 seats
    704×10= £7040
    Total money that Miss Vega will make
    £7920+£5280+£7040=£20240

  10. Q1)There 28 rows of seats.
    Q2)There will be 44 seats i think.
    Q3)1232.
    £21099.91 has been spent. if you add them altogether.
    Q4)The first 6 rows cost £30 so she will earn £7920.
    The next 6 rows which cost 20 pound she will get £5280
    The next 6 rows cost 10 this time so she will get £7040 and in total she will get £20,240.
    Q5)she will lose £20639.91 and earn £20,240.00.

  11. £8,321.17+£1,437.85=£9,759.02
    £9,759.02+£1,652.79=£11,411.81
    £11,411.81+£1,528.92=£12,940.73.
    £12,949.73+£3,832.45=£16,773.18
    £16,773.18+£1000=£17,773.18
    £17,773.18+£3,326.73=£21,099.91
    The total expense for each performance is £21,099.91

    Q1
    The total area of the theatre is 1161 metres squared.The area of the stage and the orchestra pit added together is 405 metres squared.I subtracted this from the total area of the theatre to get 756m squared.There must be a aisle in the middle that is 3cm wide. 28×3= 84 cm² plus the two 1cm wide aisle on the sides.2×28=56cm².84+56=140.
    756-140=616.Each seat takes up 25m².50×50=2500÷100=25m².Add the 50cm in front each row of seats would be 100cm long.The space left is 28m (2800cm) long.2800÷100=28 .There are 28 rows of seats.
    Q2The theatre is 27m wide.5 metres is taken up by the aisles on the sides and in the middle.This leaves 22 metres(2200 cm)for seats.Each seat is 50 cm wide.2200÷50=44.
    She can fit 44 seats in each row.
    Q3 If there are 28 rows and 44 seats in each row the n to find the amount of seats that she can have in the theatre I multiplied 44 by 28 giving me an answer of 1232 seats.
    Q4There are 264 seats in the first 6 rows.6×44=264.If she charges £30 for each seat she will make £7920.If she then charge £20 for the next 6 rows she will make £5280.Bringing the total to £13,200.If she charges £10 for the remaining seats she will make 7040 bringing the total to £20240.
    Q5Her expense total to £21,099.91 and she makes £20,240.00.This indicates a loss of £859.

  12. Question 1: How many rows of seats can Miss Vega have in her theatre?
    There are 28 rows in total.
    324÷27=12
    Stage: 27×12=324m²
    81÷27=3
    Orchestra Pit: 27×3=81m²
    12+3=15 43-15=28

    Question 2: How many seats can Miss Vega have in each row?
    There are 44 seats in total.
    1+3+1=5
    27-5=22m
    22m÷2=11m
    11m=1100cm
    1100÷50=22 seats
    On each side of the aisle that runs down the middle there are 22 seats but altogether there are 44 seats.

    Question 3: How many seats can Miss Vega have in the whole theatre?
    28×44=1232
    Miss Vega could fit 1232 seats in the whole theatre.

    Question 4: How much money will Miss Vega make from each performance if the theatre is sold out?
    44×6=264
    264×30=7920
    264×20=5280
    28-12=16
    44×16=704
    704×10=7040
    7920+5280+7040= 20240
    Miss Vega would make £20240

    Question 5: Does Miss Vega make a profit or a loss on each performance? How much does she gain/lose?
    £8321.17+ £1437.85+£1652.79+£1528.92+£3832.45+£1000.00+ £3326.73=£21099.91
    20240-21099.91=-859.91
    Miss Vega looses £859.91.

    Miss Vega previously gained £20240.

  13. Question 1:Miss Vega can have 28 rows.
    Question 2:There will be 44 seats in each row.
    Question 3: 1232
    44×28=1232
    Question 4:
    244×6=264
    264×30=7920
    264×20=5280
    28-12=16
    44×16=704
    7920+5280+7040=22,340

  14. 1.Miss Vega can have 28 rows of seats
    2.There should be 44 seats in each row
    3.There should be 1232 seats in total because if you multiply 44 and 28 you will get 1232
    4.Miss Vega gets £460 from each sold out performance.

    • Q1.
      Firstly, I worked out the answer to the orchestras and stages area result together (324+81=405)
      Secondly, I subtracted this from the total area of the theatre to get . There should
      be a middle pathway and it is 3 meters wide. 27×3= 81² and the two pathways on the sides 2×27= 52². 81+52=133². 756-133= 623. Each seat takes up 25cm². 50×50=2500²÷100=25cm²
      Add another 50cm and you will get 100cm. .The space left is 28 long.2800÷100=28.There are 28 rows of seats.
      Q2.
      There are 44 seats in total.
      1+3+1=5
      22m÷2=11m
      11m=1100cm
      1100÷50=22
      There are 22 seats that run down the middle pathway but altogether there are 44 seats.
      Q3.
      28×44=1232
      There are 1232 seats in the whole theatre.
      Q4.
      44×6=264
      264×30=7920
      264×20=5280
      28-12=16
      44×16=704
      704×10=7040
      7920+5280+7040= 20240
      That will give Miss Vega £20,240.

  15. 1. 28 rows of seats.
    2. There will be 44 seats in a row.
    1+3+1=5
    27-5=22
    22 divided by 2 =11
    11m=1100cm
    110 divide by 50=22
    22×2=44.
    There are 44 seats in a row.
    3.1232
    44×28=1232.
    4. Miss Vega loses £85891
    Miss Vega gains £20140.

  16. 1) There are 28 rows.
    Stage= 12×27=324cm²
    Orchestra pit=3×27=81cm²
    12+3=15 43-15=28
    Therefore there are 28 rows of seats.
    2)There are 44 seats in 1 complete row (both sides of the aisle)
    1+1+3=5
    27-5=22
    22÷2=11
    11÷0.5= 22
    Therefore one side of the aisle has 22 seats in a row and 44 seats in the rows altogether.

    • I did send an email earlier after you first asked for help, I sent it to an email you had sent me work from before? I will check through your work x

  17. 1.Miss Vega can have 28 rows of seats
    2.There will be 44 seats in each row
    3.There will be 1232 seats in total.
    4.Miss Vega get £460 from each sold-out performance.
    5.If Miss Vega chose the same as Mr Thorpe she will lose £20639.91,of she owns the theatre she will lose £19639.91

  18. Question 1)
    28 rows
    324 divided by 27 =12
    Stage=(12×27) 324cm²
    81 divided by 27 = 3
    Orchestral pit=(3×27) 81cm²
    12+3=15 43-15=28
    28 divided by 1=28

    Question 2)
    44 seats
    1+3+1=5
    27-5=22
    22 divided by 2=11m
    11m=1100cm
    1100 divided by 50= 22seats
    There are 22 seats on one side but in total,on one row, there are 44.
    Question 3)
    1232
    28×44=1232

    Question 4)
    44×6=264
    264×30=7920
    264×20=5280
    28-12=16
    44×16=704
    704×10=7040
    7920+5280+7040=20,240

    Question 4)
    Miss Vega makes a loss £859.91

    8321.17+1437.85+1652.79+1528.92+3832.45+1000.00+3326.73=£21,099.91

    Earlier she gained £20,240.

    21,099.91-20,240=859.91

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