document.write( "Question 102727: The tens digit of a certain number is 3 more than the units digit. The sum of the squares of the two digits is 117. Find the number. \n" ); document.write( "
Algebra.Com's Answer #74715 by bucky(2189)\"\" \"About 
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Let T represent the tens digit. Let U represent the units digit.
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\n" ); document.write( "The problem first tells you that the tens digit is 3 more than the units digit. Write this
\n" ); document.write( "in equation form as:
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\n" ); document.write( "T = U + 3
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\n" ); document.write( "Next the problem tells you that if you square each of these digits and add the squares the
\n" ); document.write( "result is 117. The tens digit squared is T^2 and the units digit squared is U^2. Add these
\n" ); document.write( "two together and set this sum equal to 117. In equation form this is:
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\n" ); document.write( "T^2 + U^2 = 117
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\n" ); document.write( "But earlier we found that T = U + 3. So in the \"squared\" equation we can substitute
\n" ); document.write( "U + 3 for T to get:
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\n" ); document.write( "(U + 3)^2 + U^2 = 117
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\n" ); document.write( "Square the U + 3 term and the equation becomes:
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\n" ); document.write( "U^2 + 6U + 9 + U^2 = 117
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\n" ); document.write( "On the left side the two U^2 terms combine and the equation becomes:
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\n" ); document.write( "2U^2 + 6U + 9 = 117
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\n" ); document.write( "To get this equation into a form that can be solved, get rid of the 117 on the right side
\n" ); document.write( "by subtracting 117 from both sides to change the equation to:
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\n" ); document.write( "2U^2 + 6U - 108 = 0
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\n" ); document.write( "Simplify this a little by dividing both sides (all terms) by 2 to reduce the equation to:
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\n" ); document.write( "U^2 + 3U - 54 = 0
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\n" ); document.write( "Notice that this can be factored to:
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\n" ); document.write( "(U + 9)(U - 6) = 0
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\n" ); document.write( "This equation will be true if either of the factors is zero, because a multiplication
\n" ); document.write( "by zero on the left side will cause the entire left side to become zero and therefore equal
\n" ); document.write( "to the right side.
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\n" ); document.write( "Setting each of the factors equal to zero results in the possible solutions being U = -9
\n" ); document.write( "and U = +6. The minus solution makes no sense ... a minus digit in a number????
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\n" ); document.write( "So the solution is that the units digit is 6. And the tens digit is 3 more than that, so
\n" ); document.write( "the tens digit is 9. The number is 96.
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\n" ); document.write( "Check ... square the 9 to get 81 and square the 6 to get 36. The sum of 81 and 36 is 117.
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\n" ); document.write( "Everything works out, so our answer is correct.
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\n" ); document.write( "Hope this helps you to understand the problem.
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