Question

Intern E.T. phoned home for some monetary help from his parents. He asked them for 23144 Asogi dollars to pay his rent. Asogi numbers are in base 6 (E.T. had only 3 fingers on each hand), and 7 Asogi dollars are equivalent to 1 American dollar. How many American dollars did E.T. pay for rent?

Answer 1

Convert 23144 in base 6 to decimals.
Divide it by 7 to convert it to dollars.

Answer 2

how do i convert between bases? is it like modular arithmetic where a normal 10 would turn to a 3?

Answer 3

Look at how the decimal number system works:
362 in decimal = 2 + 6*10 + 3*10^2 = 2 + 60 + 300 = 362

23144 in base 6 = 4 + 4*6 + 1*6^2 + 3*6^3 + 2*6^4 = ?

Answer 4

oh i get it. its 3304 in base 6

Answer 5

but wait isnt it already in base 6?

Answer 6

Yes. 23144 in base 6 = 3304 in base 10 (or in decimals).

Answer 7

how would i convert base 10 into base 6?

Answer 8

Now we have a decimal number. Divide it by 7 to convert to dollars and express the result in decimals so normal humans can understand.

Answer 9

well it is 472 dollars and thank you very much but how would base 10 be changed to base 6?

Answer 10

To convert decimal number to base 6 you have to keep dividing by 6.

Convert 3304 in decimal to a base 6 number:

6 | 3304
---------
6 | 550 R:4
|-------
6 | 91 R: 4
--------
6 | 15 R: 1
--------
2 R: 3

23144

Answer 11

the remainders make up the number because they are what is left when 3304 is divided by all the powers of 6 included in the original 3304 correct?

Answer 12

i mean the original 23144

Answer 13

correct. in the original 3304.

Answer 14

ok thank you so much i appreciate it

Answer 15

you are welcome.