A coin operated scale allows someone to weigh their self and afterthe person ste

Question

A coin operated scale allows someone to weigh their self and afterthe person steps off the scale it requires more coins.

5 girls only have one coin between them but they all want to knowtheir weight, to get around needing more coins they have 2 girlsstep on the scale at the same time, then one gets off and anothergets on. They record 10 DIFFERENT weights: 246, 241, 253, 243,256,244,251,247,250,249.
What are the weights of the girls?

You don't actually have to solve this for me if you can give me agood explanation of how to solve this. But if you do solve it,please show the work. 1st correct answer gets best answer.
**SOLUTION** Ok so I was looking at this waaay to difficultly. And so wereall of the people I asked. But thats okay because I figured it out:D, Well here it is:
Okay first we need to arrange the given numbers so they aresmallest to largest and its easier to analyze
241, 243, 244, 246, 247, 249, 250, 251, 253, 256
Now reason that the 2 smallest girls together must be thesmallest given weight. I will call the smallest girl A and thesecond smallest B
A + B = 241
Also reason that the 2 biggest girls together must be thelargest given weight. I will call the biggest girl D and the secondbiggest girl C.
C + D = 256
241 + 243 + 244 .... + 256 = 2480 2480 / 4 = 620
All the girls together weigh 620 so we can make thisequation:
A + B + M + C + D = 620 Where M is the medium sized girl.
Now we have the system of equations: A + B = 241 C + D = 256 A + B + M + C + D = 620
Now we substitute the first and second equation into the thirdto get: 241 + M + 256 = 620
Which becomes M = 123.
123 is your medium sized girl :D
Now reason that the 2nd biggest given weight, (253), must bethe medium sized girl + the biggest girl. M + D = 253 123 + D = 253 D = 130
C + D = 256 c + 130 = 256 C = 126
Now reason that your 2nd smallest given weight, (243), must bethe smallest girl + medium girl. A + M = 243 A + 123 = 243 A = 120

A + B = 241 120 + B = 241 B = 121
And now you have all your weights :D 120, 121, 123, 126, 130.
Check to make sure that they add up to 620. (they do :D)
**SOLUTION** Ok so I was looking at this waaay to difficultly. And so wereall of the people I asked. But thats okay because I figured it out:D, Well here it is:
Okay first we need to arrange the given numbers so they aresmallest to largest and its easier to analyze
241, 243, 244, 246, 247, 249, 250, 251, 253, 256
Now reason that the 2 smallest girls together must be thesmallest given weight. I will call the smallest girl A and thesecond smallest B
A + B = 241
Also reason that the 2 biggest girls together must be thelargest given weight. I will call the biggest girl D and the secondbiggest girl C.
C + D = 256
241 + 243 + 244 .... + 256 = 2480 2480 / 4 = 620
All the girls together weigh 620 so we can make thisequation:
A + B + M + C + D = 620 Where M is the medium sized girl.
Now we have the system of equations: A + B = 241 C + D = 256 A + B + M + C + D = 620
Now we substitute the first and second equation into the thirdto get: 241 + M + 256 = 620
Which becomes M = 123.
123 is your medium sized girl :D
Now reason that the 2nd biggest given weight, (253), must bethe medium sized girl + the biggest girl. M + D = 253 123 + D = 253 D = 130
C + D = 256 c + 130 = 256 C = 126
Now reason that your 2nd smallest given weight, (243), must bethe smallest girl + medium girl. A + M = 243 A + 123 = 243 A = 120

A + B = 241 120 + B = 241 B = 121
And now you have all your weights :D 120, 121, 123, 126, 130.
Check to make sure that they add up to 620. (they do :D) Okay first we need to arrange the given numbers so they aresmallest to largest and its easier to analyze
241, 243, 244, 246, 247, 249, 250, 251, 253, 256
Now reason that the 2 smallest girls together must be thesmallest given weight. I will call the smallest girl A and thesecond smallest B
A + B = 241
Also reason that the 2 biggest girls together must be thelargest given weight. I will call the biggest girl D and the secondbiggest girl C.
C + D = 256
241 + 243 + 244 .... + 256 = 2480 2480 / 4 = 620
All the girls together weigh 620 so we can make thisequation:
A + B + M + C + D = 620 Where M is the medium sized girl.
Now we have the system of equations: A + B = 241 C + D = 256 A + B + M + C + D = 620
Now we substitute the first and second equation into the thirdto get: 241 + M + 256 = 620
Which becomes M = 123.
123 is your medium sized girl :D
Now reason that the 2nd biggest given weight, (253), must bethe medium sized girl + the biggest girl. M + D = 253 123 + D = 253 D = 130
C + D = 256 c + 130 = 256 C = 126
Now reason that your 2nd smallest given weight, (243), must bethe smallest girl + medium girl. A + M = 243 A + 123 = 243 A = 120

A + B = 241 120 + B = 241 B = 121
And now you have all your weights :D 120, 121, 123, 126, 130.
Check to make sure that they add up to 620. (they do :D)

Explanation / Answer

This idea should work (I have done it on a problem likethis)
If it still doesn't work I try solving it tomorrow
If I can't get it sorry for wasting your time

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