document.write( "Question 1101958: Four times a certain number increased by three times a second number is 25. Four times the first number decreased by three times the second number is 7. Find the two numbers. \n" ); document.write( "

Algebra.Com's Answer #716594 by ikleyn(52782) $\"\"$ $\"About$

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document.write( "4x + 3y = 25,     (1)\r\n" );
document.write( "4x - 3y =  7.     (2)\r\n" );
document.write( "---------------------------Subtract eq(2) from eq(1). You will get\r\n" );
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document.write( "6y = 25 - 7 = 18  ===>  y =  = 3.\r\n" );
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document.write( "Then from (1),  4x = 25 - 3y = 25 - 3*3 = 25 - 9 = 16;\r\n" );
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document.write( "Hence, x =  = 4.\r\n" );
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document.write( "Answer.  First number is  4;  second number is  3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The good style in solving such problems is to notice/(to observe) immediately from the condition that the difference
\n" ); document.write( "between two combinations is 6 times the second number, which, in turn, is the difference 25-7 = 18,
\n" ); document.write( "and to deduce from it MENTALLY that y= 3, without writing any equations.\r
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\n" ); document.write( "\n" ); document.write( "This problem is for mental solution, and it would be ideally if you see the solution immediately/instantly.\r
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