An automaker of new cars recommends an oil change after the first 5000 miles and every 3000 miles thereafter. if you plan to drive the car 250 miles a week, how many oil changes will you need the first year?

You need 3 oil changes for first year

Given that, automaker of new cars recommends an oil change after the first 5000 miles and every 3000 miles thereafter

We know that there are 52 weeks in a year

You plan to drive the car 250 miles a week, therefore

1 week = 250 miles

52 weeks = 52 x 250 = 13000 miles

So you drive 13000 miles for first year

Given that,

Cars recommends an oil change after the first 5000 miles and every 3000 miles thereafter

So, you will have 1st oil change at 5000 miles.

Now after 5000 miles you have 1 oil change.

13000 miles - 5000 miles = 8000 miles

Remaining miles is 8000

Then second change at 3000 miles

8000 - 3000 = 5000 miles

Then again third change at 3000 miles.

5000 - 3000 = 2000 miles

Therefore, you need 3 oil changes for first year