Question

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?

Answer 1

46 cm

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.