document.write( "Question 1024485: Word problem:-
\n" ); document.write( "A three digit number is equal to 17 times the sum of its digits. If 198 is added to the original number,
\n" ); document.write( "the digits get interchanged. The addition of the first & the third digit is 1 less than the middle digit.
\n" ); document.write( "Find the original number. (steps required) \n" ); document.write( "

Algebra.Com's Answer #639876 by MathTherapy(10552) $\"\"$ $\"About$

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Word problem:-
\n" ); document.write( "A three digit number is equal to 17 times the sum of its digits. If 198 is added to the original number,
\n" ); document.write( "the digits get interchanged. The addition of the first & the third digit is 1 less than the middle digit.
\n" ); document.write( "Find the original number. (steps required)
\n" ); document.write( "

Number: .\r\n" );
document.write( "Don't you think you need to make an attempt? It's not that difficult to try something!\r\n" );
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document.write( "After your E-Mail, here's the solution:\r\n" );
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document.write( "Let the hundreds, tens, and units digits, be H, T, and U, respectively. From clue 1, we get:\r\n" );
document.write( "100H + 10T + U = 17(H + T + U)		\r\n" );
document.write( "100H + 10T + U = 17H + 17T + 17U		\r\n" );
document.write( "83H - 7T - 16U = 0 -------- eq (i)	\r\n" );
document.write( "		\r\n" );
document.write( "From clue 2, we get:\r\n" );
document.write( "100H + 10T + U + 198 = 100U + 10T + H		\r\n" );
document.write( "99H - 99U = - 198		\r\n" );
document.write( "99(H – U) = 99(- 2)  ------- Dividing by GCF, 99		\r\n" );
document.write( "H – U = - 2 -------- eq (ii)\r\n" );
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document.write( "Finally, clue 3 tells us that: \r\n" );
document.write( "H + U = T - 1		\r\n" );
document.write( "H - T + U = - 1 ------ eq (iii)		\r\n" );
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document.write( "- 7H + 7T - 7U = 7 ---- Multiplying eq (iii) by - 7		\r\n" );
document.write( " 83H - 7T - 16U = 0 --- eq (i)		\r\n" );
document.write( " 76H - 23U = 7 -------- Adding eqs (iii) & (i) ------- eq (iv)\r\n" );
document.write( "\r\n" );
document.write( "    H –   U = - 2 ----- eq (ii)\r\n" );
document.write( "- 23H + 23U =  46 ----- Multiplying eq (ii) by – 23 ------- eq (v) 		\r\n" );
document.write( "  76H – 23U =   7 ----- eq (iv)\r\n" );
document.write( "        53H = 53 ------ Adding eqs (v) & (iv)\r\n" );
document.write( "          H, or hundreds digit = , or 1		\r\n" );
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document.write( "1 - U = - 2 -------- Substituting 1 for H in eq (ii)		\r\n" );
document.write( "  - U = - 2 - 1		\r\n" );
document.write( "  - U = - 3\r\n" );
document.write( "    U, or units digit = , or 3\r\n" );
document.write( "		\r\n" );
document.write( "1 – T + 3 = - 1 ------- Substituting 1 for H, and 3 for U in eq (iii)		\r\n" );
document.write( "    4 – T = - 1\r\n" );
document.write( "      - T = - 1 – 4\r\n" );
document.write( "      - T = - 5\r\n" );
document.write( "        T, or tens digit = , or 5

\n" ); document.write( "Number: $\"highlight_green%28153%29\"$ \n" ); document.write( "

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