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Complete the input-output tables for the two machines. Machine 1: input -> x3 -> +5 -> output. Machine 2: input -> +5 -> x3 -> output. Use the given inputs.

Mathematics

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Step-by-step solution

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Let's complete the input-output tables based on the given rules.

For the first machine (Input →×3→+5→\to \times 3 \to + 5 \to Output):

  1. Calculate the output for input 6.

    (6×3)+5=18+5=23(6 \times 3) + 5 = 18 + 5 = 23
  2. Calculate the output for input 8.

    (8×3)+5=24+5=29(8 \times 3) + 5 = 24 + 5 = 29
  3. Calculate the output for input 10.

    (10×3)+5=30+5=35(10 \times 3) + 5 = 30 + 5 = 35
  4. Calculate the output for input 12.

    (12×3)+5=36+5=41(12 \times 3) + 5 = 36 + 5 = 41

    The outputs for the first machine are:

    • Input 6: 23\boxed{23}
    • Input 8: 29\boxed{29}
    • Input 10: 35\boxed{35}
    • Input 12: 41\boxed{41}

    For the second machine (Input →+5→×3→\to + 5 \to \times 3 \to Output):

  5. Calculate the output for input 4.

    (4+5)×3=9×3=27(4 + 5) \times 3 = 9 \times 3 = 27
  6. Calculate the output for input 6.

    (6+5)×3=11×3=33(6 + 5) \times 3 = 11 \times 3 = 33
  7. Calculate the output for input 8.

    (8+5)×3=13×3=39(8 + 5) \times 3 = 13 \times 3 = 39
  8. Calculate the output for input 10.

    (10+5)×3=15×3=45(10 + 5) \times 3 = 15 \times 3 = 45
  9. Calculate the output for input 12.

    (12+5)×3=17×3=51(12 + 5) \times 3 = 17 \times 3 = 51

    The outputs for the second machine are:

    • Input 4: 27\boxed{27}
    • Input 6: 33\boxed{33}
    • Input 8: 39\boxed{39}
    • Input 10: 45\boxed{45}
    • Input 12: 51\boxed{51}
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