An auditorium has 80 rows of seats and the number of seats per row increases at a constant rate. If there are 32 seats in the 8th row, and 68 seats in the 20th row, how many seats are in the last row?

Question

Mathematics

Jazmin Harrison

19 December, 08:22

An auditorium has 80 rows of seats and the number of seats per row increases at a constant rate. If there are 32 seats in the 8th row, and 68 seats in the 20th row, how many seats are in the last row?

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Answers (1)

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Quintin · Answer 1

To find how many seats in the 80th row, you need to figure out the pattern from the 8th row to the 20th row.

To do this, you can create a table showing possibilities from the 8th to the 20th.

I started with 32 at the 8th and added 2 each time. This was only 56 by the 20th.

Then I added 3, and this got me to 68 by the 20th row.

Then you can work backwards to find how many seats in the 1st row. I got 11.

From here you can create an equation that you could use to solve for the 80th row.

11 + 3 (r - 1), where r is the number of rows.

Substitute in 80 for r.

11 + 3 (80 - 1)

11 + 237

248 seats

There are 248 seats in the 80th row.