document.write( "Question 670782: Bads is thinking of two numbers. One number is 7 more than the other number. The product of the numbers is 60. What are the numbers? \n" ); document.write( "
Algebra.Com's Answer #417176 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "Problem: \r\n" );
document.write( "Bads is thinking of two numbers .one number is 7more than the other number .the product of \r\n" );
document.write( "the number is 60.what are the numbers?\r\n" );
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document.write( "Solution:\r\n" );
document.write( "You can solve this a non-algebra way or an algebra way.\r\n" );
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document.write( "I. The non-algebra method.\r\n" );
document.write( "Think of a number pair whose product is 60. Check to see if the difference is 7.\r\n" );
document.write( "(1, 60) --> 1 * 60 = 60 ---> 60 - 1 = 59 \r\n" );
document.write( "(2,30) --> 2 * 30 = 60 --> 30 - 2 = 28\r\n" );
document.write( "(3, 20) --> 3 * 20 = 60 --> 20 - 3 = 17\r\n" );
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document.write( "Continue in this manner until you find the pair of numbers whose product is 60 and whose difference is 7.\r\n" );
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document.write( "(4, 15) --> 4 * 15 = 60 --> 15 - 4 = 11\r\n" );
document.write( "(5, 12) --> 5 * 12 = 60 --> 12 - 5 = 7\r\n" );
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document.write( "Bingo! The two numbers are 5 and 12.\r\n" );
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document.write( "II. The algebra method\r\n" );
document.write( "Let x be the smaller number.\r\n" );
document.write( "Let y be the larger number.\r\n" );
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document.write( "The product of the two numbers is 60, so x * y = 60.\r\n" );
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document.write( "The difference between the numbers is 7, so y - x = 7.\r\n" );
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document.write( "Let's rewrite this second equation in \"y=\" form by adding x to both sides.\r\n" );
document.write( "y - x = 7\r\n" );
document.write( "y = 7 + x\r\n" );
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document.write( "Substitute 7 + x for y in the first equation.\r\n" );
document.write( "x * y = 60\r\n" );
document.write( "x * (7 + x) = 60\r\n" );
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document.write( "Solve for x. Clear the parentheses by using the distributive property.\r\n" );
document.write( "7x + x^2 = 60\r\n" );
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document.write( "We have a quadratic equation. Subtract 60 from both sides and rearrange the terms in \r\n" );
document.write( "descending order.\r\n" );
document.write( "x^2 + 7x - 60 = 0\r\n" );
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document.write( "Rewrite the equation in factored form. We want two factors with a product of -60, and a \r\n" );
document.write( "difference of 7. The factors are 12 and -5.\r\n" );
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document.write( "(x + 12)(x - 5) = 0\r\n" );
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document.write( "Solve.\r\n" );
document.write( "x = -12 or x = 5\r\n" );
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document.write( "Try each solution in the real-world problem.\r\n" );
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document.write( "If x = 5, then the smaller number is 5 and the larger number is 12 (because 12 - 5 = 7).\r\n" );
document.write( "The product of 5 and 12 is 60, so this pair works.\r\n" );
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document.write( "If x = -12, then the smaller number is -12 and the larger number is -5 \r\n" );
document.write( "(because -12 - (-5) = 7). The product of -5 and -12 is 60, so this number pair also works.\r\n" );
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document.write( "So, you have two possible number pairs: -5 and -12 or 5 and 12. \r\n" );
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document.write( "Hope this helps,\r\n" );
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document.write( "Mrs.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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