Question 580366: The sum of two numbers is 77 and the product of the two numbers is 1440.
I found 30 x 48 = 1440 but their sum is 78
Where did I go wrong?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First, list out the factors of  :
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
-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
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*1440 = 1440
2*720 = 1440
3*480 = 1440
4*360 = 1440
5*288 = 1440
6*240 = 1440
8*180 = 1440
9*160 = 1440
10*144 = 1440
12*120 = 1440
15*96 = 1440
16*90 = 1440
18*80 = 1440
20*72 = 1440
24*60 = 1440
30*48 = 1440
32*45 = 1440
36*40 = 1440
(-1)*(-1440) = 1440
(-2)*(-720) = 1440
(-3)*(-480) = 1440
(-4)*(-360) = 1440
(-5)*(-288) = 1440
(-6)*(-240) = 1440
(-8)*(-180) = 1440
(-9)*(-160) = 1440
(-10)*(-144) = 1440
(-12)*(-120) = 1440
(-15)*(-96) = 1440
(-16)*(-90) = 1440
(-18)*(-80) = 1440
(-20)*(-72) = 1440
(-24)*(-60) = 1440
(-30)*(-48) = 1440
(-32)*(-45) = 1440
(-36)*(-40) = 1440
Now let's add up each pair of factors to see if one pair adds to  :
| 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 |
From the list above, we see that the row highlighted in red is our answer.
So
32 + 45 = 77
and
32*45 = 1440
which means that the two numbers are 32 and 45.
Answer by josmiceli(19441)  (Show Source):
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