Linear Word Problem

Question

you want to buy a used car for business purposes, with the following models to select from. Model A cost $13,600 and depreciates $500 a year. Model B costs $16,000 and depreciates $800 a year.

 

A). for each model write an equation to determine resale value V of this car after X years for use.

 

B). Write a system of linear equations that can be used to determine how many years will have to expire in order for both cars to have the same resale value.

Answer 1

Car A has the value of V=13600-500x since it starts at 13600 and for every year, its value goes down by 500.

Car B has the value of V=16000-800x since it starts at 16000 but for every year, its value decreases by 800.

 

So if you just substitute the expression for v into the second expression, you get an equation that you can solve.

 

13600 - 500x = 16000 - 800x.      Add 800x to both sides to get

13600 + 300x = 16000                 subtract 13600 from both sides to get

             300x = 2400                   divide both sides by 300 to get

                  x = 8

 

This means that in 8 years, the two cars will have the same value. You can check by pugging in 8 into the 2 equations.

 

V = 13600 - 500(8) = 13600 - 4000 = 9600

V = 16000 - 800(8) = 16000 - 6400 = 9600

 

So in 8 years, they will both be worth $9600.

 

Hope this helped