Question

The automaker of your new car recommends an oil change following the first 5,000 miles and then every 3,000 miles thereafter. If you plan to drive the car 250 miles a week, how many oil changes will you need the first year?

Answer 1

To determine the number of oil changes needed in the first year, calculate the total number of miles driven in a year and divide by the number of miles between oil changes. The answer is 3 oil changes.

Step-by-step explanation:

To determine the number of oil changes you will need in the first year, we need to calculate the number of weeks in a year and divide it by the number of miles between oil changes.

There are 52 weeks in a year and you plan to drive the car 250 miles per week, so the total number of miles you will drive in a year is 52 × 250 = 13,000 miles.

The first oil change is recommended after 5,000 miles, so you will need an oil change after 5,000 miles and then every 3,000 miles thereafter.

The number of oil changes you will need in the first year is (13,000 - 5,000) ÷ 3,000 = 8 ÷ 3 = 2.67. Since you can't have a fractional oil change, you will need 3 oil changes in the first year.

Answer 2

To determine how many oil changes you will need the first year, you can calculate the number of miles driven the first year and then use that to determine how many groups of 3000 miles you will drive after the first 5000 miles.

1. 52 x 250 = 13000 miles

2. 13000 miles - 5000 miles (1 oil change) = 8000 miles

3. 8000 miles - 3000 miles (1 oil change) - 3000 miles (1 oil change) = 2000 miles

The first year, you will need 3 oil changes.