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Undersea explorers discover a second sentient race living on Earth. This species is scientifically much more advanced but cannot share its discoveries because it uses a different system of units. Human scientists first try to convert between units of length: they measure a meter as 12 bap'ai and 2 bok'ai or alternatively 10 bap'ai and 10 bok'ai. In centimeters, how much distance is 5 bap'ai and 3 bok'ai?

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sqdancefan

Answer:

  46 cm

Step-by-step explanation:

Let p represent the length in cm of 1 bap'ai; let k represent the length in cm of 1 bok'ai. Then we have ...

  12p +2k = 100

  10p +10k = 100

Subtracting the second equation from 5 times the first, we get ...

  5(12p +2k) -(10p +10k) = 5(100) -(100)

  50p = 400

  p = 8 . . . . cm

Then the second equation tells us ...

  10(8) +10k = 100

  10k = 20

  k = 2 . . . . cm

Then 5p+3k = 5(8) +3(2) = 46 cm.

The distance 5 bap'ai and 3 bok'ai is 46 cm.

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