document.write( "Question 825067: three times the difference of eight and twice a number is five times the number. \n" ); document.write( "
Algebra.Com's Answer #497053 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem:\r\n" );
document.write( "Three times the difference of eight and twice a number is five times the number.\r\n" );
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document.write( "Solution:\r\n" );
document.write( "It's not clear what you are being asked to do here. It might be that you only need to translate \r\n" );
document.write( "the sentence into an algebraic equation. You may also need to solve it. I'll walk you through \r\n" );
document.write( "both steps.\r\n" );
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document.write( "Let's break this sentence into pieces and translate as we go. First, we define a variable:\r\n" );
document.write( "Let n be \"a number.\"\r\n" );
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document.write( "We translate the phrase \"twice a number\" as \"2 times n,\" or 2n.\r\n" );
document.write( "We translate the phrase \"five times the number\" as 5 times n, or 5n.\r\n" );
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document.write( "\"The difference of eight and twice a number\" means subtraction, so we have 2n - 8.\r\n" );
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document.write( "\"Three times the difference\" is 3 times (2n - 8), or 3(2n - 8).\r\n" );
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document.write( "When we translate sentences into algebra, the word \"is\" means equality, so we use an\r\n" );
document.write( "equals sign. Let's put this all together,\r\n" );
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document.write( "3(2n - 8) = 5n.\r\n" );
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document.write( "Now, let's solve for n:\r\n" );
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document.write( "Use the distributive property to clear the parentheses.\r\n" );
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document.write( "6n - 24 = 5n\r\n" );
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document.write( "Combine like terms by subtract 6n from both sides of the equation. (6n-6n=0)\r\n" );
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document.write( "6n -24 - 6n = 5n - 6n\r\n" );
document.write( "-24 = -n\r\n" );
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document.write( "Divide both sides of the equation by -1. ((-n)/(-1)=n)\r\n" );
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document.write( "(-24)/(-1) = (-n)/(-1)\r\n" );
document.write( "24 = n\r\n" );
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document.write( "Rewrite this equation with in \"n=\" form.\r\n" );
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document.write( "n = 24\r\n" );
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document.write( "The number is 24. Check your answer in the original English sentence.\r\n" );
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document.write( "Twice the number is 2 * 24 = 48\r\n" );
document.write( "The difference between 8 and 48 is 48 - 8 = 40\r\n" );
document.write( "Three times forty is 3 * 40 = 120.\r\n" );
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document.write( "Five times 24 is 5 * 24 = 120.\r\n" );
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document.write( "Both halves of the sentence equal 120, so 24 is the correct number.\r\n" );
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document.write( "Good luck!\r\n" );
document.write( "Mrs Figgy\r\n" );
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