Question

On the main floor of a theatre the number of seats per row increases at a constant rate. Jack counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20

Answer 1

Answer: 65 seats in row 20

Step-by-step explanation: 3 = 31, 6 = 37 the difference is 3 rows but 6 seats so its going up 2 every row therefor you need 14 rows after row 6 so 14 * 2 + 37 = 65 seats

Answer 2

By finding a linear equation, we will see that on the row 20 there are 65 seats.

How many seats are in row 20?

Here we have a linear relationship, that can be written as:

y = a*x + b

Where a is the slope and b the y-intecept.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), the slope is:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

In this case, we have points of the form (row, seats), and the two points that we have are:

(3, 31) and (6, 37)

So the slope is:

$a = \frac{37 - 31}{6 - 3} = 2$

So the equation is:

y = 2*x + b

To find the value of b, we replace one of the points in the equation. If we use the first one, we have x = 3 and y = 31, so:

31 = 2*3 + b

31 = 6 + b

31 - 6 = 25 = b

The equation is:

y = 2x + 25

The number of seats in row 20 is what we get if we replace x by 20, then:

y = 2*20 + 25 = 65

If you want to learn more about linear equations, you can read:

https://brainly.com/question/1884491