document.write( "Question 1207681: A school orders $99$ textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?\r
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Algebra.Com's Answer #845685 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let the price of a book be ABCD.EF.\r\n" );
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document.write( "Then 100 books would cost ABCDEF.00\r\n" );
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document.write( "So we subtract the price of 1 book from ABCDEF.00 and get G38254.1H,\r\n" );
document.write( "the price of 99 books.\r\n" );
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document.write( "So we have this subtraction\r\n" );
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document.write( "     A B C D E F.0 0\r\n" );
document.write( "       - A B C D.E F \r\n" );
document.write( "     ---------------\r\n" );
document.write( "     G 3 8 2 5 4.1 H\r\n" );
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document.write( "So G=A, 10-F=H and 9-E=1, so E=8\r\n" );
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document.write( "     A B C D 8 F.0 0\r\n" );
document.write( "       - A B C D.8 F \r\n" );
document.write( "     ---------------\r\n" );
document.write( "     A 3 8 2 5 4.1 H\r\n" );
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document.write( "F cannot be 0, since that would make H be 10.\r\n" );
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document.write( "Depending on whether we will have to borrow from the 8 above the C,\r\n" );
document.write( "C must be either 2 or 3, so those two cases are:\r\n" );
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document.write( "    A B 2 D 8 F.0 0             A B 3 D 8 F.0 0\r\n" );
document.write( "      - A B 2 D.8 F               - A B 3 D.8 F \r\n" );
document.write( "    ---------------             ---------------\r\n" );
document.write( "    A 3 8 2 5 4.1 H             A 3 8 2 5 4.1 H\r\n" );
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document.write( "Either way, we know we'll have to borrow from the B to make the 2 a 12.\r\n" );
document.write( "So 12-A=8 so A is 4.  And since we borrow from B, B=4\r\n" );
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document.write( "So these two cases become\r\n" );
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document.write( "    4 4 2 D 8 F.0 0             4 4 3 D 8 F.0 0\r\n" );
document.write( "      - 4 4 2 D.8 F               - 4 4 3 D.8 F \r\n" );
document.write( "    ---------------             ---------------\r\n" );
document.write( "    4 3 8 2 5 4.1 H             4 3 8 2 5 4.1 H\r\n" );
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document.write( "Now we see that D can only be 6:\r\n" );
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document.write( "    4 4 2 6 8 F.0 0             4 4 3 6 8 F.0 0\r\n" );
document.write( "      - 4 4 2 6.8 F               - 4 4 3 6.8 F \r\n" );
document.write( "    ---------------             ---------------\r\n" );
document.write( "    4 3 8 2 5 4.1 H             4 3 8 2 5 4.1 H\r\n" );
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document.write( "That tells us that we did have to borrow from the 8,\r\n" );
document.write( "so that eliminates the second case and makes F having to\r\n" );
document.write( "have been scratched with a zero over it, which makes F=1\r\n" );
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document.write( "    4 4 2 6 8 1.0 0            \r\n" );
document.write( "      - 4 4 2 6.8 1                \r\n" );
document.write( "    ---------------             \r\n" );
document.write( "    4 3 8 2 5 4.1 H\r\n" );
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document.write( "So we finally see that H=9.\r\n" );
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document.write( "    4 4 2 6 8 1.0 0            \r\n" );
document.write( "      - 4 4 2 6.8 1                \r\n" );
document.write( "    ---------------             \r\n" );
document.write( "    4 3 8 2 5 4.1 9\r\n" );
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document.write( "So the missing digits are 4 and 9.\r\n" );
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document.write( "[Can you believe that a textbook would cost $4426.81?]  \r\n" );
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document.write( "Edwin
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