SOLUTION: a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?

Question 1196225: a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?

Found 4 solutions by Alan3354, ikleyn, math_tutor2020, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?
---------------
92 - 3*52 = a negative number.
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.
a gymnasium has 52 rows of seats. the last row contains 92 seats.
if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?
~~~~~~~~~~~~~~~~

The problem describes an IMPOSSIBLE situation, which never may happen.

The problem is FATALLY DEFECTIVE and is only good to throw it to the closest garbage bin.

It came from a bad source.

        Inform the source about this fatal deficiency.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

We have an arithmetic sequence because of the gap of 3 seats per row.

Counting down the sequence involves -3, so going up the sequence involves +3 or 3.
a = first term
d = 3 = common difference

first row = a
second row = a+3
third row = a+3+3 = a+3(2)
fourth row = a+3+3+3 = a+3(3)
fifth row = a + 3+3+3+3 = a + 3(4)
and so on

nth row = a+3(n-1)
We have n = 52 rows in total
That 52nd row has 92 seats

nth row = a+3(n-1)
52nd row = a+3(52-1)
92 = a+3(52-1)
92 = a+3(51)
a+3(51) = 92
a+153 = 92
a = 92-153
a = -61

The arithmetic sequence is: {-61, -58, -55, ..., 86, 89, 92} which consists of 52 terms

As you can see, we run into a problem. There's no way to have a negative number of seats in the first row. Or any row really.
Your teacher made a typo somewhere.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?

If what you meant was that "each row has 3 fewer seats than the row ~~behind~~ in front of it,"
the AP would be: , and the first row would have 245 seats.
RELATED QUESTIONS
The balcony of a theater has 12 rows of seats. The last row contains 8 seats, and each of (answered by jorel555,ikleyn)
A theater contains 25 rows of seats. The first row contains 25 seats. Each succeeding row (answered by richwmiller)
Each of the rows in the auditorium has two more seats than the row in front of it. If the (answered by stanbon)
a 40 row theater has 10 seats in the front row. the second row has 11 seats. if each row... (answered by josmiceli)
a conference hall has 20 rows of seats .the first row contains 20 seats,the second row... (answered by ikleyn)
how many rows are in the corner section of a tennis court stadium containing 255 seats if (answered by greenestamps)
A rectangular classroom seats 72 students. When the seats are rearranged with three more... (answered by lwsshak3)
A local civic theater has 22 seats in the first row and 21 rows in all. Each successive... (answered by Boreal)
A theatre is set up in such a way that there are 20 seats in the first row and 4... (answered by Earlsdon)