Can Anyone Help Me with This Math Problem?

Question

I have been working on this two days. I need help plz.

"You have five bales of hay. For some reason, instead of being weighed individually, they were weighed in all possible combinations of two; bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4, etc. The weight of each of these combinations were written down and arranged in numerical order without keeping track of which weight matched each pair of bales. The weights in kilograms were 80, 82, 83, 84, 85, 86, 87, 88, 90, and 91."

Now, I have to find out how much each bale weighs, and if there is more than one possible combination, and then explain it. I was trying to randomly assign numbers to the bales of hay, but I can't get them all to fit, and I don't know any other way to do it. Any mathematical geniuses out there?

Answer 1

This is a little tough, but to help I added all the weights 80...91 and the sum is 856. This is 4x the sum of all five bales 1, 2, 3, 4, and 5. The sum of the bales is 214.

Did you try assigning the bales letters and presuming they were in order? Such as a+b+c+d+e=428, a
If a+b+c+d+e=214 and a+b=80 and d+e=91 then subtract the latter two equations to get c=43.
Then, if a+c=82, subtract c=43 to get a=39.
Then, if a+b=80, subtract a=39 to get b=41.
Then, if c+e=90, subtract c=43 to get e=47.
Then, if d+e=91, subtract e=47 to get d=44.

Proof/check:
a+b=80, a+c=82, a+d=83, a+e=86, b+c=84, b+d=85, b+e=88, c+d=87, c+e= 90, and d+e=91.

Answer 2

karruttopp ...Take a deep breath and read the question carefully. Especially this part>>>
"The weight of each of these combinations were written down and arranged in numerical order without keeping track of which weight matched each pair of bales"......

And 'Maegical'...... how can u conclude its half of 856? What 'karruttopp has done is correct (although, it assumes the order as is), so u can add his answer and conclude too that it's far below 428................ooooo no, u edited ur answer again !!.. This time u make sense.. Good Job (Y)...


It's a nice tricky question....

Answer 3

First we start by assigning variables to each bale of hay.
1=x, 2=y, 3=z, 4=r, and 5=s

x+y=80
x+z=82
x+r=83
x+s=84
y+z=85
y+r=86
y+s=87
z+r=88
z+s=90
r+s=91

Write x in terms of y; x=80-y
80-y+z=82
z-y=2
z+y=85
2z=87
z=43.5
plug and chug away now
x+43.5=82, x=38.5
z+y=85, y=41.5
z+r=88, r=44.5
z+s=90, s=46.5

There you go, next time just take a deep breath and break it down.