Here are some new distances with given lengths to help Cecil cross the tightrope. Find at least two ways to get Cecil across for each situation. Write your solutions in symbolic form.    

1. Span of tightrope: $19$ feet     Given lengths: $4$, $5$, $7$ feet.  

   Hint (a):

   How can you add or subtract any number of $4$'s, $5$'s, and $7$'s to make $19$?

   Answer (a):

   $4+4+4+7$, or $3(4)+7$, is one way of solving this problem. Can you find at least one more solution?

   Explore part (a) with the eTool below.
   Click the link at right for the full version of the eTool: 6-113a HW eTool 

2. Span of tightrope: $25$ feet     Given lengths: $3$, $6$, $7$ feet.  

   Hint (b):

   If you multiply $6$ by $3$, how far from $25$ is the product? Answer that question and use it as a starting point for your solution. Remember to check your work!

   Explore part (b) with the eTool below.
   Click the link at right for the full version of the eTool: 6-113b HW eTool

3. Span of tightrope: $23$ feet     Given lengths: $5$, $2$, $9$ feet.  

   Hint (c):

   This problem is very similar to parts (a) and (b). Try starting with one number and see how close you can get to $23$ using just that number. Then see if one of the other lengths can help you finish.

   Explore part (c) with the eTool below.
   Click the link at right for the full version of the eTool:  6-113c HW eTool