5-2-a-3-5-the-addition-on-the-left-is-in-base-6-find-a-1001-

Question Number 44324 by Rio Michael last updated on 26/Sep/18

5 2 a

+ 3 5

___t h e a d d i t i o n o n t h e l e f t i s i n b a s e 6 . f i n d a .

1001

Answered by MJS last updated on 27/Sep/18

in base 6 similar to what we learned in

primary school :

1001 - 0035 = ?

5 + 2 = 11, write 2, keep 1 in mind

1001 - 0035 = 2

3 + 1 = 4

4 + 2 = 10, write 2, keep 1 in mind

1001 - 0035 = 22

0 + 1 = 1

1 + 5 = 10, write 5, keep 1 in mind

1001 - 35 = 522

0 + 1 = 1

1 + 0 = 1, so {we}^{'} re ready

a = 2

Answered by MrW3 last updated on 27/Sep/18

{(52 a)}_{6} = 5 \times 6^{2} + 2 \times 6^{1} + a \times 6^{0} = 192 + a

{(35)}_{6} = 3 \times 6^{1} + 5 \times 6^{0} = 23

{(1001)}_{6} = 1 \times 6^{3} + 0 \times 6^{2} + 0 \times 6^{1} + 1 \times 6^{0} = 217

192 + a + 23 = 217

\Rightarrow a = 2

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