Question

Assume there is a linear relationship between the curb weight of a car (in thousands of kilograms) and its combined mileage (in miles per gallon). The Hummer H2 has a weight of 3 thousand kg and mileage of 9 mpg, while a Ford Taurus sedan weighs 1.9 thousand kg and gets 21 mpg. What is the mileage of a Chevy Cavalier weighing 1.1 thousand kg?

Answer 1

Answer: The mileage of a Chevy Cavalier weighing 1.1 thousand kg is 29.72 mpg.

Explanation:

if there is a linear relationship between two variables x and y , then we represent this relation in the form of equation as :
`y= mx+c` (*)

, where m = rate of change of y with respect to x

c= Constant or the value of y when x=0.

We assume there is a linear relationship between the curb weight of a car (in thousands of kilograms) and its combined mileage (in miles per gallon).

Let y= combined mileage (in miles per gallon)

x= curb weight of a car (in thousands of kilograms)

When x= 3 thousand kg , y = 9 mpg

⇒
`9= m(3)+c` [Put values in (*)]

⇒
`9= 3m+c--------(1)`

When x= 1.9 thousand kg , y = 21 mpg

⇒
`21= m(1.9)+c` [Put values in (*)]

⇒
`21= 1.9m+c--------(2)`

Eliminate the equation (1) from (2) , we get

`1.9m-3m=21-9`

`-1.1m=12\\\Rightarrow\ m=(12)/(-1.1)=(-120)/(11)`

Put value of m in (1) , we gte

`9= 3((-120)/(11))+c`

`9= (-360)/(11)+c\\\Rightarrow\ c=9+(360)/(11)=(459)/(11)`

Substitute the value of m and c in (*) , we get

`y= (-120)/(11)x+(459)/(11)`

When x= 1.1

`y= (-120)/(11)(1.1)+(459)/(11)`

`y= (-120)/(11)((11)/(10))+(459)/(11)`

`y=-12+(459)/(11)=(327)/(11)\approx29.72`

Hence, the mileage of a Chevy Cavalier weighing 1.1 thousand kg is 29.72 mpg.