Chapter 8.2, Problem 35PPS

To determine

To find: number of seats in the section.

Answer to Problem 35PPS

Total number of seats is 665.

Explanation of Solution

Given information:

One section of a movie theater has 26 seats in the first row, 35 seats in the second row, 44 seats in third row, and so on. There are 10 rows of seats.

Calculation:

The sequence is

26, 35, 44,…

The different in number of rows is 1

  

Number of rows $\left(r\right)$	1	2	3
Number of seats $\left(s\right)$	26	35	44

  

The difference in number of seats is 9.

Since the difference in number of seats is 9, the equation is $s=9r$

However, add 17 to get $s$ value.

So, $s$ value is three times $r$ value plus 17

Therefore, equation is $s=9r+17$ .

To find number of seats in ${10}^{th}$ row

Substitute $r=10$ in $s=9r+17$

  $\begin{array}{c}s=9\left(10\right)+17\\ =90+17\\ =10\end{array}$

To find total number of seats, that is to find sum of 10 numbers 26+35+44+…+107 Formula is

  $\frac{n\left(\text{first}\text{number+last}\text{number}\right)}{2}$

Here,

  $\begin{array}{c}\frac{10\left(26+107\right)}{2}=\frac{10\left(133\right)}{2}\\ =5\left(133\right)\\ =665\end{array}$

Therefore, total number of seats is 665.