Question

An airplane has room for 300 coach- fair seats. It can replace any 3 coach seats with 2 first class seats. Suppose the airplane is configured with x coach seats and y first class seats. (Assume no space is wasted)

A) if y=0, what is the value of x? Explain the significance in terms of The airplane’s seat configuration.

B)if x=0 ,what is the value of y? Explain the significance in terms of The airplane’s seat configuration.

C)it can be shown that y is a linear function of x. Sketch a graph y versus x, labeling both axis-intercepts.

D) find a formula for y in terms of x

Answer 1

Given

An airplane has room for 300 coach- fair seats.

It can replace any 3 coach seats with 2 first class seats.

To proof

let coach seats = x

first class seats =y

As given in the question airplane has room for 300 coach- fair seats

i.e their is no first class seat.

First point becomes (300,0 )

replace 3 coach seats with 2 first class seats (Given in question )

second point becomes (297,2 )

we get two points (300,0 ) and (297,2 ) .

FORMULA

Equation of line with two point

`(y-y_(1))= (y_(2)-y_(1))/(x_(2)-x_(1))(x-x_(1))`

put the points value in the above equation

`(y-0)= (2-0)/(297-300)(x-300)`

`y = (2)/(-3) (x-300)`

sloving the above equation

we get the equation

`y = (-2)/(3) x + 200`

Proof of (A)

Given : y=0

find the value of x

put this value in

`y = (-2)/(3) x + 200`

we get

`(2)/(3) x = 200`

x = 300

Proof of (B)

Given : x =0

find out the value of y

put these value in the equation

`y = (-2)/(3) x + 200`

y = 200

Proof of (C)

Show that y is a linear function of x.

y is a linear function of x this is shown in the table and graph given below.

Proof of (D)

find a formula for y in terms of x

the equation

`y = (-2)/(3) x + 200`

Hence proved