Question 1207681
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The amount on the bill is "A38,254.1B", where A and B are digits that are not known.<br>
The bill is for 99 textbooks that all have the same price, so A382541B is divisible by 99.<br>
The number is divisible by 99 if and only if it is divisible by both 9 and 11.<br>
To be divisible by 9, the sum of the digits must be divisible by 9:<br>
A+3+8+2+5+4+1+B = 23+(A+B)<br>
For that sum to be divisible by 9, A+B can only be either 4 or 13.<br>
<b>(1) A+B = 4 or A+B = 13</b><br>
The number is divisible by 11 if and only if the two sums of alternating digits are either equal or differ by a multiple of 11.<br>
A+8+5+1 = A+14; 3+2+4+B = B+9<br>
If A and B are positive single digit numbers with A+B=4, those two sums can't be equal.  So A+B is 13.<br>
We need to have A+14 = B+9, and A+B=13:<br>
A+B=13 --> B=13-A
A+14 = B+9
A+14 = (13-A)+9
A+14 = 22-A
2A = 8
A = 4
B = 13-A = 9<br>
ANSWER: The obscured digits are A=4 and B=9<br>
CHECK: $438,254.19/99 = $4426.81<br>