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Suppose that a and b are digits in base d > 6 such that \(\overline{AB}_d+\overline{AA}_d=162_d\)

Find \(A_d-B_d\) in base d.

Thanks in advance!

 Dec 28, 2020
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72_8  +  77_8  = 162_8

 

7_8    -   2_8   = 5_8

 

Note: The first base I tried was base 8. I converted 162_8 to base 10 = 114. Then I tried 2 numbers that add up to 93. I tried 45 + 48 = 93. Then I converted 45 to base 7 =63. And similarly, converted 48 to base 7 = 66. Then added 72 + 77 (base 8) =162_8. That is how I arrived at the answer above.

 Dec 28, 2020

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