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Home > MC1 > Chapter 4 > Lesson 4.1.3 > Problem 4-32

4-32.

Each of the diagrams below represents a sequence for an acrobat on a tightrope. Each letter represents the unknown length of a trick. For each part below, figure out how far the acrobat travels during each trick (that is, the length represented by each letter). Show how you know.

  1. Find .
    Two equal length line segments. Top, 3 sections labeled, x, 7, and x.  Bottom, labeled 13.

    If is the same as , can you think of a way to find the value of ?

    To find the value of both 's combined, we can subtract from .

    Now you know that two 's are equal to . Can you find the value of one ?

  1. Find .
    Two equal length line segments. Top, 4 sections labeled, j, ,j, 15 and j.  Bottom, labeled 27.

    Do you think you can use a similar strategy as in part (a)? Remember, try to find the value of just one j.

    is the same as . Can you find the value of ?

    . Remember to show how you know!

  1. Find .
    Two equal length line segments. Top, 6 sections, labeled, n, n, 6, 6, 6 and 6.  Bottom, 44.

    Remember that is the same as . This simplification should make finding easier.

    If two 's equal , how much is one ?