document.write( "Question 580366: The sum of two numbers is 77 and the product of the two numbers is 1440. \r
\n" ); document.write( "\n" ); document.write( "I found 30 x 48 = 1440 but their sum is 78 \r
\n" ); document.write( "\n" ); document.write( "Where did I go wrong? \n" ); document.write( "

Algebra.Com's Answer #371215 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, list out the factors of $\"1440\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,32,36,40,45,48,60,72,80,90,96,120,144,160,180,240,288,360,480,720,1440\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-8,-9,-10,-12,-15,-16,-18,-20,-24,-30,-32,-36,-40,-45,-48,-60,-72,-80,-90,-96,-120,-144,-160,-180,-240,-288,-360,-480,-720,-1440\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"1440\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*1440 = 1440
\n" ); document.write( "2*720 = 1440
\n" ); document.write( "3*480 = 1440
\n" ); document.write( "4*360 = 1440
\n" ); document.write( "5*288 = 1440
\n" ); document.write( "6*240 = 1440
\n" ); document.write( "8*180 = 1440
\n" ); document.write( "9*160 = 1440
\n" ); document.write( "10*144 = 1440
\n" ); document.write( "12*120 = 1440
\n" ); document.write( "15*96 = 1440
\n" ); document.write( "16*90 = 1440
\n" ); document.write( "18*80 = 1440
\n" ); document.write( "20*72 = 1440
\n" ); document.write( "24*60 = 1440
\n" ); document.write( "30*48 = 1440
\n" ); document.write( "32*45 = 1440
\n" ); document.write( "36*40 = 1440
\n" ); document.write( "(-1)*(-1440) = 1440
\n" ); document.write( "(-2)*(-720) = 1440
\n" ); document.write( "(-3)*(-480) = 1440
\n" ); document.write( "(-4)*(-360) = 1440
\n" ); document.write( "(-5)*(-288) = 1440
\n" ); document.write( "(-6)*(-240) = 1440
\n" ); document.write( "(-8)*(-180) = 1440
\n" ); document.write( "(-9)*(-160) = 1440
\n" ); document.write( "(-10)*(-144) = 1440
\n" ); document.write( "(-12)*(-120) = 1440
\n" ); document.write( "(-15)*(-96) = 1440
\n" ); document.write( "(-16)*(-90) = 1440
\n" ); document.write( "(-18)*(-80) = 1440
\n" ); document.write( "(-20)*(-72) = 1440
\n" ); document.write( "(-24)*(-60) = 1440
\n" ); document.write( "(-30)*(-48) = 1440
\n" ); document.write( "(-32)*(-45) = 1440
\n" ); document.write( "(-36)*(-40) = 1440\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to $\"77\"$ :\r
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First Number	Second Number	Sum
1	1440	1+1440=1441
2	720	2+720=722
3	480	3+480=483
4	360	4+360=364
5	288	5+288=293
6	240	6+240=246
8	180	8+180=188
9	160	9+160=169
10	144	10+144=154
12	120	12+120=132
15	96	15+96=111
16	90	16+90=106
18	80	18+80=98
20	72	20+72=92
24	60	24+60=84
30	48	30+48=78
32	45	32+45=77
36	40	36+40=76
-1	-1440	-1+(-1440)=-1441
-2	-720	-2+(-720)=-722
-3	-480	-3+(-480)=-483
-4	-360	-4+(-360)=-364
-5	-288	-5+(-288)=-293
-6	-240	-6+(-240)=-246
-8	-180	-8+(-180)=-188
-9	-160	-9+(-160)=-169
-10	-144	-10+(-144)=-154
-12	-120	-12+(-120)=-132
-15	-96	-15+(-96)=-111
-16	-90	-16+(-90)=-106
-18	-80	-18+(-80)=-98
-20	-72	-20+(-72)=-92
-24	-60	-24+(-60)=-84
-30	-48	-30+(-48)=-78
-32	-45	-32+(-45)=-77
-36	-40	-36+(-40)=-76

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\n" ); document.write( "\n" ); document.write( "From the list above, we see that the row highlighted in red is our answer.\r
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\n" ); document.write( "\n" ); document.write( "So \r
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\n" ); document.write( "\n" ); document.write( "32 + 45 = 77\r
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\n" ); document.write( "\n" ); document.write( "and\r
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\n" ); document.write( "\n" ); document.write( "32*45 = 1440\r
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\n" ); document.write( "\n" ); document.write( "which means that the two numbers are 32 and 45. \n" ); document.write( "

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