SOLUTION: Please help me solve this problem: Nick, Ben, and Joseph are volunteering at their local pumpkin patch. Walking in they found a scale to weigh the pumpkins, but the scale started a

Algebra ->  Equations -> SOLUTION: Please help me solve this problem: Nick, Ben, and Joseph are volunteering at their local pumpkin patch. Walking in they found a scale to weigh the pumpkins, but the scale started a      Log On


   

Question 847747: Please help me solve this problem: Nick, Ben, and Joseph are volunteering at their local pumpkin patch. Walking in they found a scale to weigh the pumpkins, but the scale started at 100kg. The three boys decided to weigh themselves, though they knew they would not be over that amount, even Nick who knew that he weighed the most, but they decided to weigh themselves in pairs anyway. These are their calculations.
Ben+Joseph=132kg
Joseph+Nick=151kg
Nick+Ben=137kg








Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Assign identifyable variables to make equations this way:

b+j=132kg
-
j+n=151kg
-
n+b=137kg

Coefficients in that system on each variable are 1.
Subtract second equation from the first equation:
b%2Bj-j-n=132-151
b-n=-19
n-b=19

Use this resulting equation with the third, as yet unused equation for a simpler system:
-
n+b=137
-
n-b=19
-

That simpler system is perfectly set to use Elimination Method to get a value for n. Add the two equations to eliminate b:
n%2Bb%2Bn-b=137%2B19
2n=156
highlight%28n=78%29. NICK'S WEIGHT.

Now use either of the two equations with n and b to get Ben's weight:
n%2Bb=137
b=137-n
b=137-78
highlight%28b=59%29 BEN'S WEIGHT.

You can find Josephs weight... Right?
(Use one of the original equations with only Ben's weight now being unknown.)