document.write( "Question 76252: Hi, I need help on getting this answer - Three times the larger of 2 numbers increased by 4 times the smaller is 205. Six times the larger plus 3 times the smaller is 270. Find the numbers.
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Algebra.Com's Answer #54718 by psbhowmick(878) $\"\"$ $\"About$

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Let larger number = x and smaller number = y.
\n" ); document.write( "Three times the larger number (= 3x) increased by 4 times the smaller = 3x + 4y.
\n" ); document.write( "This value is given 205.
\n" ); document.write( "So, 3x + 4y = 205 __________(1)\r
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\n" ); document.write( "\n" ); document.write( "Six times the larger number (= 6x) plus 3 times the smaller = 6x + 3y.
\n" ); document.write( "This value is given 270.
\n" ); document.write( "So, 6x + 3y = 270
\n" ); document.write( "or 2x + y = 90 ___________(2)\r
\n" ); document.write( "\n" ); document.write( "We now have to solve equations (1) and (2) to find x and y.
\n" ); document.write( "Multiplying both sides of eq (2) with 4 and subtracting both sides of eq (1) from it
\n" ); document.write( "4(2x + y) - (3x + 4y) = 4*90 - 205
\n" ); document.write( "(8x + 4y) - (3x + 4y) = 360 - 205
\n" ); document.write( "5x = 155
\n" ); document.write( "x = 31\r
\n" ); document.write( "\n" ); document.write( "So from (2)
\n" ); document.write( "2*31 + y = 90
\n" ); document.write( "or y = 90 - 62 = 28\r
\n" ); document.write( "\n" ); document.write( "Thus the numbers are 31 and 28. \n" ); document.write( "

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