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The robotics team uses wire to build their robot and controller.

Before building anything, the team has a roll of 9 5/12 feet of wire.
To build the robot, the team uses 6 1/2 feet of wire.
To build the controller, the team uses 3/4 foot of wire.

After building, how many feet of wire does the team have left?

A. 2 2/12feet
B. 3 1/12 feet
C. 3 8/12 feet
D. 7 3/12 feet

1 answer

To find out how much wire the team has left after building the robot and the controller, we can follow these steps:

  1. Convert the mixed numbers to improper fractions:

    • The initial amount of wire: \( 9 \frac{5}{12} \) feet

      • \( 9 = \frac{108}{12} \)
      • \( 9 \frac{5}{12} = \frac{108}{12} + \frac{5}{12} = \frac{113}{12} \)

    • The amount used for the robot: \( 6 \frac{1}{2} \) feet

      • \( 6 \frac{1}{2} = 6 + 0.5 = 6 + \frac{1}{2} = 6 + \frac{6}{12} = \frac{72}{12} + \frac{6}{12} = \frac{78}{12} \)

    • The amount used for the controller: \( \frac{3}{4} \) feet

      • Convert \( \frac{3}{4} \) to twelfths: \( \frac{3}{4} = \frac{9}{12} \)

  2. Calculate the total wire used:

    • Total wire used = Wire used for robot + Wire used for controller
    • Total wire used = \( \frac{78}{12} + \frac{9}{12} = \frac{87}{12} \)

  3. Calculate the remaining wire:

    • Remaining wire = Initial wire - Total wire used
    • Remaining wire = \( \frac{113}{12} - \frac{87}{12} = \frac{26}{12} \)

  4. Convert the remaining wire back to a mixed number:

    • \( \frac{26}{12} = 2 \frac{2}{12} \)
    • Simplifying \( \frac{2}{12} \) gives \( \frac{1}{6} \), so:
    • Remaining wire = \( 2 \frac{1}{6} \) feet

Comparing with the provided options, the closest match is:

A. 2 2/12 feet (which is equivalent to 2 1/6 feet)

Thus, the teams have 2 2/12 feet of wire left.