Video Transcript
Marie bought a used car with 50,000 miles. She thinks that she travels 250 miles every week. Which of the following represents the distance, in miles, that she will have traveled 𝑛 weeks after buying the car? A) 50,250 plus 𝑛. B) 50,250 minus 𝑛. C) 250 plus 50,000 times 𝑛. D) 50,000 plus 250 times 𝑛.
The variable 𝑛 represents the number of weeks after Marie has bought the car. When 𝑛 equals one, Marie has had the car for one week. And since she thinks she travels 250 miles every week when 𝑛 equals one, Marie would have put 250 new miles on the car. The car had 50,000 miles. And in week one, Marie put 250 miles on the car. And so we can say that when 𝑛 equals one, the car should have 50,250 miles. We can use this information to test the other four options. When 𝑛 equals one in option A, you would have 50,250 plus one. So Marie would have driven 50,251 miles. This equation cannot be correct. It’s adding the number of weeks to the number of miles plus the first week.
When we move on to option B, we see subtraction. We have 50,250 minus the number of weeks that Marie has had the car. And this also doesn’t make sense. Using this equation, the number of miles that Marie had driven would go down by one every week. What about option C? Option C is multiplying the number of weeks by 50,000. This equation is saying that Marie drives 50,000 miles every week and that the car started with 250 miles. This is not true. And it leads us to option D. Marie started with 50,000 miles and added 250 every week. So we multiply 250 by the number of weeks she’s had the car.
