# Answer to Question #26099 in Combinatorics | Number Theory for kim

Question #26099

find the base of the numeral system in which 26-18=9(express your answer in base 10).

Expert's answer

The number 26 in its respective base b is equal to 2*b+6.

If the number 26 were in base 10, then it would be equal to 2*10+6.

The number 19 in its respective base b is equal to 1*b+9.

If the number 19 were in base 10, then it would be equal to 1*10+9.

Compose the equation 2b+6-(b+8)=9, b-2=9, b=11. Therefore the base of system is 11.

If the number 26 were in base 10, then it would be equal to 2*10+6.

The number 19 in its respective base b is equal to 1*b+9.

If the number 19 were in base 10, then it would be equal to 1*10+9.

Compose the equation 2b+6-(b+8)=9, b-2=9, b=11. Therefore the base of system is 11.

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## Comments

Assignment Expert10.10.14, 19:11Dear beckfordburger. Thank you for correcting us.

beckfordburger01.10.14, 11:26the answer to the question 'find the base of the numeral system in which 26-18=9(express your answer in base 10)' is 11

in numeral base 11:

26=((11x2)+6)=28

18=((11x1)+8)=19

28-19=9

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