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Chapter 8: Q. 8.181 (page 1016)

A car鈥檚 value varies inversely with its age. Elena bought a two-year-old car for $20,000.

鈸� Write the equation of variation.

鈸� What will be the value of Elena鈥檚 car when it is 5 years old?

Short Answer

Expert verified

(a)v=40000a

(b) $8000

Step by step solution

01

Part (a) Step 1. Given information.

We have been given that a car鈥檚 value varies inversely with its age. Elena bought a two-year-old car for $20,000.

We have to write the equation of variation.

02

Part (a) Step 2. Assume the variables and write the formula for inverse variation and then substitute the given values for the variables. 

Let

v=car鈥�svaluea=car鈥�sage

We can write v=ka.

Substitute v=20000,a=2.

20000=k2

03

Part (a) Step 3. Solve for the constant of variation and write the equation of variation.

20000=k2k=2(20000)=40000

Therefore, we can write:

v=40000a

04

Part (b) Step 1. Put a=5 in the formula v=40000a and solve.

v=40000av=400005=8000

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