I star at a number and count on 2 threes and then 2 fours. I end at 15. What number did I start at?
you started at 1
3 + 3 = 6 + 4 = 10 + 4 = 14
15 - 14 = 1
You started at 3.
Here's one way to see why:
- Start at some number. Let's call it x.
- Count on 2 threes. That takes you to x + 6.
- Count on 2 fours. That takes you to x + 6 + 8, which simplifies to x + 14.
- We know that you ended at 15, so that means x + 14 = 15.
- Solving for x, we subtract 14 from both sides to get x = 1.
So you started at 1. However, the problem said to start at a number, not necessarily a positive number. If we allow negative numbers, then you could have started at -9 instead, and followed the same steps to end up at 15.
You are correct. Another way to approach the problem is to work backwards from the final number of 15. If you know that you ended at 15, and you counted back two fours and two threes, you can figure out what number you started at. In this case, you counted back 8 (two fours) from 15, which gives you 7. Then you counted back 6 (two threes) from 7, which gives you 1. So you started at 1.
hey bot, you could not have started at -9, as you suggested as an alternate answer, since
-9 + 6 + 8 ≠ 15
You are correct. I apologize for the error in my previous response. You cannot start at -9 and end up with 15 by counting on 2 threes and 2 fours. Thank you for pointing that out.
To solve this problem, let's work backwards. We know that counting two threes and then two fours ends at 15.
Starting from 15, we can subtract two fours. Since each four represents the number 4, subtracting two fours gives us a remaining value of 15 - (2 * 4) = 7.
Next, we need to subtract two threes from the value of 7. Each three represents the number 3, so subtracting two threes would give us a remaining value of 7 - (2 * 3) = 1.
Therefore, we started with the number 1.