Certainly! Let's solve the problem step by step.
We are given the following information:
1. Waylon stopped with 217 more rungs left to climb.
2. The total number of rungs on the ladder is 239.
We need to determine how many rungs Waylon had already climbed.
First, let's denote the number of rungs Waylon had already climbed by [tex]\( x \)[/tex].
Since the total number of rungs on the ladder is 239, and Waylon still had 217 rungs left to climb, we can set up the equation:
[tex]\[ \text{(number of rungs climbed)} + \text{(number of rungs left to climb)} = \text{(total number of rungs)} \][/tex]
Mathematically:
[tex]\[ x + 217 = 239 \][/tex]
Now, let's solve for [tex]\( x \)[/tex]:
Subtract 217 from both sides of the equation:
[tex]\[ x + 217 - 217 = 239 - 217 \][/tex]
[tex]\[ x = 22 \][/tex]
So, Waylon had already climbed 22 rungs.
Now, let's look at the given choices to see which ones correctly represent this word problem:
Choice A: [tex]\( x + 217 = 239 \)[/tex]
- This equation matches the one we set up and solved. Therefore, it is correct.
Choice B: [tex]\( 239 - 217 = \)[/tex]
- This is a subtraction that shows the remaining rungs subtracted from the total rungs. This calculates the number of climbed rungs as:
[tex]\[ 239 - 217 = 22 \][/tex]
It also represents our solution correctly.
Choice C: [tex]\( x - 217 = 239 \)[/tex]
- This equation doesn't fit the word problem. Subtracting the number of rungs Waylon had left to climb from the number he had already climbed to equal the total number of rungs does not make sense. Incorrect.
Choice D: [tex]\( 239 + 217 = x \)[/tex]
- This equation does not represent the word problem. Adding the remaining rungs to the total rungs to find [tex]\( x \)[/tex] would give a value much larger than the total number of rungs, which is not logical. Incorrect.
Choice E: Both A and B are correct
- Since both A and B are correct, this choice is indeed correct.
Thus, the correct answer is:
[tex]\[ \boxed{\text{E. Both A and B are correct}} \][/tex]
