Good job, Melody and guest !!!!
Here's my solution :
Let a > b > c > c > d > e where these are the weights of the girls
And each is weighed 4 times.....and their total weight = 1212 lbs
So we have that 4 ( a + b + c + d + e) = 1212 ⇒ a + b + c + d + e = 303
And here are the equations that we are sure of
The two heaviest = a + b = 129 (1)
Since a > b, then a + c > b + c....so a + c is the second heaviest weight
a + c = 125 (2)
The two lightest = d + e = 114 (3)
Since c > d, then c + e > d + e ......so c + e is the second lightest weight
c + e = 116 (4)
Subtract (2) from (1) = b - c = 4 ⇒ b = c + 4
Subtract (4) from (3) = c - d = 2 ⇒ c = d + 2
So this implies that b = d + 6
Now.....add (1) and (2)
2a + b + c = 254 ⇒ b + c = 154 - 2a ⇒ (d + 6) + (d + 2) = 154 - 2a ⇒
2d + 8 = 154 - 2a → 2a + 2d = 246 ⇒ a + d = 123 ⇒ a = 123 - d
Similarly.....add (3) + (4) and we have that
c + d + 2e = 230 ⇒ (d + 2) + d = 230 - 2e ⇒ 2d = 228 - 2e ⇒ d = 114 - e ⇒ e = 114 - d
So
a + b + c + d + e = 303 and substituitng, we have
(123 - d) + (d + 6) + (d + 2) + d + (114 - d) = 303
d + 245 = 303
d = 58
So
a = 123 - d = 65 lbs
b = d + 6 = 64 lbs
c = d + 2 = 60 lbs
d = 58 lbs
e = 114 - d = 56 lbs