document.write( "Question 406668: I have two questions, the 1st one is:\r
\n" ); document.write( "\n" ); document.write( "#1. The product of two numbers is 10 less than 16 times the smaller. if twice the smaller is 5 more than the larger number, find the two numbers.\r
\n" ); document.write( "\n" ); document.write( "I'm having trouble with the first one. The second problem is this:\r
\n" ); document.write( "\n" ); document.write( "#2. The area of a rectangular field is 162 sq. m. and its length is twice its width. Find the dimensions of the field.\r
\n" ); document.write( "\n" ); document.write( "In number 2 I did this:\r
\n" ); document.write( "\n" ); document.write( "Let x = width
\n" ); document.write( " 2x = length\r
\n" ); document.write( "\n" ); document.write( " (2x)(x) = 162
\n" ); document.write( "> 2x^2 = 162
\n" ); document.write( "> 2x^2/2 = 162/2
\n" ); document.write( "> x^2 = 81
\n" ); document.write( "> x = 9\r
\n" ); document.write( "\n" ); document.write( "I just wanna ask if my answer is correct or do I have to continue and it like this:
\n" ); document.write( "> 2x
\n" ); document.write( "> 2(9)
\n" ); document.write( "> = 18\r
\n" ); document.write( "\n" ); document.write( "Looking forward for your response. \n" ); document.write( "
Algebra.Com's Answer #286890 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
#1. The product of two numbers is 10 less than 16 times the smaller. if twice the smaller is 5 more than the larger number, find the two numbers.
\n" ); document.write( ".
\n" ); document.write( "Let x = smaller of two numbers
\n" ); document.write( "and y = larger of two numbers
\n" ); document.write( ".
\n" ); document.write( "from: \"The product of two numbers is 10 less than 16 times the smaller\" we get:
\n" ); document.write( "xy = 16x-10 (equation 1)
\n" ); document.write( "from: \"twice the smaller is 5 more than the larger number\" we get:
\n" ); document.write( "2x = y+5 (equation 2)
\n" ); document.write( ".
\n" ); document.write( "Solving equation 1 for y:
\n" ); document.write( "xy = 16x-10
\n" ); document.write( "y = (16x-10)/x
\n" ); document.write( "Plug above into equation 2 and solve for x:
\n" ); document.write( "2x = y+5
\n" ); document.write( "2x = (16x-10)/x+5
\n" ); document.write( "multiplying both sides by x:
\n" ); document.write( "2x^2 = (16x-10)+5x
\n" ); document.write( "2x^2 = 21x-10
\n" ); document.write( "2x^2 - 21x + 10 = 0
\n" ); document.write( "(2x-1)(x-10) = 0
\n" ); document.write( "x = {1/2, 10}
\n" ); document.write( "throw out the 1/2 leaving:
\n" ); document.write( "x = 10
\n" ); document.write( ".
\n" ); document.write( "to find y, plug above into:
\n" ); document.write( "xy = 16x-10
\n" ); document.write( "10y = 160-10
\n" ); document.write( "10y = 150
\n" ); document.write( "y = 15
\n" ); document.write( ".
\n" ); document.write( "solution: the two numbers are 10 and 15\r
\n" ); document.write( "\n" ); document.write( ".
\n" ); document.write( "#2. The area of a rectangular field is 162 sq. m. and its length is twice its width. Find the dimensions of the field.
\n" ); document.write( "In number 2 I did this:
\n" ); document.write( "Let x = width
\n" ); document.write( "2x = length
\n" ); document.write( "(2x)(x) = 162
\n" ); document.write( "> 2x^2 = 162
\n" ); document.write( "> 2x^2/2 = 162/2
\n" ); document.write( "> x^2 = 81
\n" ); document.write( "> x = 9
\n" ); document.write( "I just wanna ask if my answer is correct or do I have to continue and it like this:
\n" ); document.write( "> 2x
\n" ); document.write( "> 2(9)
\n" ); document.write( "> = 18 \r
\n" ); document.write( "\n" ); document.write( "Yes, you must -- because the problem is asking for \"the dimensions\".
\n" ); document.write( "x gives you only the width
\n" ); document.write( "you need to find the length also
\n" ); document.write( "complete answer would be 9 meters by 18 meters
\n" ); document.write( "(don't forget your units)
\n" ); document.write( " \n" ); document.write( "
\n" );