Question

someone help please, giving brainlist to anyone who answers <3

Answer 1

Answer:

65 seats

Step-by-step explanation:

1. Approach

To answer this question, one has to find the rate at which seats are added to each row. Then one must find the number of seats in the first row. Using this information, one can form an equation to find out how many seats are in any given row when given the row number. Finally, one can substitute (20) into the equation to find out how many seats are in the row (20).

2.Find the rate at which seats are added

One is given the row number and the corresponding number of seats in the row. This information is presented in the formate ($x,y$), as the following is,

(3, 31), (6, 37)

Where (x) is the row number and (y) is the number of seats.

To find the rate at which seats are added, one must solve for the rate of change. This can be done using the following formula,

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

Substitute in the given information and solve for the rate of change,

$\frac{37-31}{6-3}$

Simplify,

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

Seats are added at a rate of (2) seats per row.

3. Find the equation

The easiest way to write the equation of this situation is to use the equation of a line is in the slope-intercept form. This form is as follows,

$y=mx+b$

Where (m) is the slope of the line and (b) is the (y-intercept). As one found in (step (2)) the slope of the line is (2). Substitute this into the equation,

$y=2x+b$

One is given that (3, 31) is a part of this scenario, substitute this point into the equation and solve for the unknown,

$(31)=2(3)+b$

Simplify,

$31 = 6+b$

Inverse operations,

$31=6+b\\25=b$

Substitute this into the equation to complete the equation,

$y=2x+25$

4.Find how many seats are in the row (20)

Now that one has the equation to find the number of seats where (x) represents the row number and (y) represents the number of seats. Substitute in the row number (20) to solve to find the number of seats in the row.

$y=2x+25$

$y=2(20)+25$

Simplify,

$y=2(20)+25\\y=40+25\\y=65$