Question

James is training for a marathon. Every week, he increases the distance he runs by 15%. If James is running 8.5 miles this week, how far will he be running 2 weeks from now?

I did 30/100=x/8.5 . I thought that if I did 30 (for 2 weeks) instead of 15 (1 week) I could get a straight answer. But the answer choices I have are:

A. 15.3 miles. B. 10.2 miles
C. 11.24 miles. D. 9.8 miles

Answer 1

I see where you went wrong.
If, say, you increased the price of something by 20% that's not the same as if you increased the price by 10% today and then 10% again tomorrow.

If it was €100 to begin with
10% would be €10.
Your total is now €110
If you get 10% for the second day that would be €11 not €10
Your total is now €121

If you added 20% from the start.
20% of 100 is €20
So the total would be €120 which is not the same as the answer you get by adding 10% twice.

The same is true for increasing the distance.
It's increased by 15% which brings the total distance to 115% of the original.
The 15% again which of 115% is 17.25% which makes the total increase 132.25% not 30% as you have.

x = 8.5*132.25/100

Answer 2

*makes the total increase 32.35% not 30% as you have

Answer 3

Good for you! You tried what seemed a logical method -- but you found it didn't work! You learned something! :-)

Let's see of this works.

8.5 * 1.15 = 9.775 the second week
9.775 * 1.15 = 11.24 the third week