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# Please someone help me with a math problem? solving for how many seats total in a theater?

Help :( I tried to draw it out lol but its confusing me still

A theater has 11 seats in the first row. each row has 3 more seats than the row in front of it.

if the theatre has 35 rows, how many seats in total are in the theatre?

thank you for your help.

really?? that was easy. (to the first answer)

I figured the first answer couldn't be right lol.

Something wasn't making sense.

thanks.

### 4 Answers

- Native HanoianLv 47 years agoFavorite Answer
The first answer is very wrong because by taking 11 + 3*35

that would mean there's just one row with 11 seats while the other 35 rows have only 3 seats each.

Answer to porblem:

The number of seat per row is 11 + 3*(n-1) with n is the number of row.

For example:

First row: n=1 => seats = 11+3*(1-1) = 11

So on, the number of seats for the:

Second row = 11 + 3*1

Third row = 11 + 3*2

....

...

35th row = 11 + 3*34

The total seats in the theatre is determined as the sum of seats in all rows which is:

First row + second row + ....+ 35th row

= 11*35 + 3*(1+ 2 + 3 +....+34)

= 385 + 3*[ (1+34) + (2 + 33) +....+ (16+17)]

= 385 + 3*[ (35) + (35) + ....+ (35)]

that makes "35" repeating 16 times

= 385 + 3*16*35

= 385 + 1680

= 2065

Conclusion: if the theater has 35 rows, there'll be 2065 seats.

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- 7 years ago
That other guy is wrong by the way, you don't do 11 + 3 x 35, or that just means there are 14 seats in every row. The answer is 487, because you do (11 + 3)35 - 3, -3 being 34 and not counting the first one, because it does not have an extra 3 seats.

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- mingoLv 44 years ago
You want two equations. Let A = Adults and C = youngsters So complete adults + whole children = 500, thus A + C = 500 The 2nd equation involves price $43 per adult and $28 for kids and the total money is 16805. So 2nd equation is 43A + 28C = 16805 A + C = 500 43A + 28C = 16805 Rearrange the 1st equation to remedy for A. A = 500 - C and substitute into the 2d equation. 43(500 - C) + 28C = 16805 Simplify to get 21500 - 43C + 28C = 16805 simplify additional -15C = -4695 and C = 313 so you had 313 children Adults would be 500 - 313 or 187

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