Answer to Question #219226 in Algebra for Shenice

Question

Andrew's parents follow a regular schedule for taking care of their car. They change the oil every 3 000 km, rotate the tyres every 10 000 km and replace the wiper blades every 15 000 km. After how many kilometres will they first have to change the oil, rotate the tyres and replace the wiper blades all at once? 

Answer 1

$$3000a=10000b=15000c, a, b, c\in Z^+$$

$$3a=10b=15c$$

$$a=5c$$

$$b=1.5c$$

$c=1$ does not satisfy the equation $b=1.5c$ , because $1.5$ is not integer.

$c=2: a=10, b=3$

$$3000(10)=10000(3)=15000(2)=30000$$

They first will have to change the oil, rotate the tyres and replace the wiper blades all at once after 30000 kilometres.