What Do They Weigh? A math problem (corrected)

Lord Burn
Posers and Puzzles 26 Sep '03 15:06
1. 26 Sep '03 15:06
Five people want to weigh themselves on a coin-operated scale. They want to pay only once. Two of the people climb onto the scale, drop in a coin, and record their combined weight. One person gets off, another person gets on, and they record their combined weight. This continues until the people have the following weights recorded: 188, 192, 196, 199, 203, 204, 207, 208, 212, and 219.

1.Show all work and determine what each person weighs.

2. 26 Sep '03 16:40
Originally posted by Lord Burn
Five people want to weigh themselves on a coin-operated scale. They want to pay only once. Two of the people climb onto the scale, drop in a coin, and record their combined weight. One person gets off, another person gets on, and they record their combined weight. This continues until the people have the following weights recorded: 188, 192, 196, 1 ...[text shortened]... ll work and determine what each person weighs.

Label the peoples' weights in order a, b, c, d and e where a is the lightest.

The sum of all the weighings is 2028
each person has been on the scale 4 times, ie 2028 = 4(a+b+c+d+e)
therefore a+b+c+d+e = 2028/4 = 507

188, the lightest total, must be the weight of the two lightest people, i.e 188 = a+b

219, the heaviest total, must the weight of the two heaviest people, i.e 219 = d+e

so a+b+d+e = 188+219 = 407

Because, from above, a+b+c+d+e =507, c must weigh 100

192, the second lightest total, must be the weight of the lightest person and the 3rd lightest person, i.e 192 = a+c, so a = 92

212, the second heaviest total, must be the weight of the heaviest person and the third heaviest person, i.e. 212 = c+e, so e = 112

Above we stated that a+b = 188, now we know a = 92 so b = 96

Also above we stated that d + e = 219, now we know e = 112, so d = 107

To summarise, the weights are 92, 96, 100, 112, 107 ðŸ™‚
3. 29 Sep '03 14:26
thank you, i am a tiger.