document.write( "Question 951991: Use the clue to complete the equation using some or all of the digits 2, 4, and 6.
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Algebra.Com's Answer #582362 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
Use the clue to complete the equation using some or all of the digits 2, 4, and
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document.write( "?×?5?=26??\r\n" );
document.write( "A×B5C=26DE\r\n" );
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document.write( "That gives the equation\r\n" );
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document.write( "A(100B+50+C)=2600 + 10D + E\r\n" );
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document.write( "{A,C} is not equal to {2,4} since that would make E=8.\r\n" );
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document.write( "So we have only 4 cases to consider:\r\n" );
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document.write( "Case 1: A and C, respectively either equals 2 and 6, respectively, and E=2 \r\n" );
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document.write( "Case 2: A and C, respectively either equals 6 and 2, respectively, and E=2 \r\n" );
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document.write( "Case 3: A and C, respectively either equals 4 and 6, respectively, and E=4 \r\n" );
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document.write( "Case 4: A and C, respectively either equals 6 and 4, respectively, and E=4 \r\n" );
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document.write( "A and C, respectively equals 2 and 4 and E=4\r\n" );
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document.write( "Case 1:  (A,C) equals (4,6) and E=2 \r\n" );
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document.write( "2×B56=26DE\r\n" );
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document.write( "4(100B+50+6)=2602 + 10D  \r\n" );
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document.write( "2(100B+56)=2602 + 10D\r\n" );
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document.write( "200B+112=2602 + 10D\r\n" );
document.write( "200B = 2490 + 10D\r\n" );
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document.write( "20B = 249 + 10D\r\n" );
document.write( "20B-10D = 249\r\n" );
document.write( "The left side is divisible by 10 but the \r\n" );
document.write( "right side is not. \r\n" );
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document.write( "Case 2:  {A,C} equals {6,2} and E=2 \r\n" );
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document.write( "6×B52=26D2\r\n" );
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document.write( "6(100B+50+2)=26D2  or 6(100B+50+2)=26D2\r\n" );
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document.write( "6(100B+52)=2602 + 10D\r\n" );
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document.write( "200B+312=2602 + 10D\r\n" );
document.write( "200B = 2290 + 10D\r\n" );
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document.write( "20B = 229 + D\r\n" );
document.write( "The left side is divisible by 20 but the \r\n" );
document.write( "right side cannot be unless D could be 11.\r\n" );
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document.write( "Case 3:  (A,C) equals (6,4} and E=2 \r\n" );
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document.write( "6×B52=26D2\r\n" );
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document.write( "6(100B+50+2)=26D2  or 6(100B+50+2)=26D2\r\n" );
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document.write( "6(100B+52)=2602 + 10D\r\n" );
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document.write( "600B+312=2602 + 10D\r\n" );
document.write( "600B = 2290 + 10D\r\n" );
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document.write( "60B = 229 + D\r\n" );
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document.write( "The left side is divisible by 60 but the \r\n" );
document.write( "right side cannot be unless D could be 11,\r\n" );
document.write( "which it cannot.\r\n" );
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document.write( "Case 4:  (A,C) equals (4,6) and E=4 \r\n" );
document.write( "4×B56=26D4\r\n" );
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document.write( "4(100B+50+6)=26D4\r\n" );
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document.write( "4(100B+50+6)=26D4  or 6(100B+50+4)=26D4\r\n" );
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document.write( "4(100B+56)=2604 + 10D\r\n" );
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document.write( "400B+224=2604 + 10D\r\n" );
document.write( "400B = 2380 + 10D\r\n" );
document.write( "40B = 238 + D\r\n" );
document.write( "D = 40B - 238\r\n" );
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document.write( "The right side is divisible by 2 but not by 4, so D=2\r\n" );
document.write( "2 = 40B - 238\r\n" );
document.write( "240 = 40B\r\n" );
document.write( "  6 = B\r\n" );
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document.write( "So the solution is 4×656=2624.\r\n" );
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document.write( "Edwin
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