Can this weight equation be solved?

Question

Let's say you and another person decided to lose weight together, but the other person didn't want you to know their weight, so all they would tell you is what percentage the BOTH of you have lost. Could you knowing your starting weight, your ending, your weight loss and the overall percentage of you and your partner's weight loss determine your partner's starting weight? Ex. you lost 10 lbs starting from 200 lbs, ending at 190 (or 5%) and your combined loss with your partner is overall at 10%.

Answer 1

They lost 5% as well, but there is no telling what that amount is. They could have weighed 200 lbs as well, meaning they lost 10 lbs, or they could have weighed 220, and lost 11. There is no telling without one more variable.

Answer 2

You started at Y pounds, they started at T pounds.

You lost y pounds and they lost t pounds.

total percentage lost = (y+t)/(Y+T)

You have two unknowns, t and T,

so all you can tell is the relation between them.

Example given:

.10 = (10 + t)/(200 + T)

.10 (200 + T) = 10 + t

20 + .10 T = 10 + t

10 = t - .10 T

t = 10 + .10 T

They lost 10 lbs + 10% of their original weight. <== what you can tell

For example:

Their original weight / amount lost

150  25  (total loss: 35/350)

160  26  (total loss: 36/360)

170  27  etc.

180  28

190  29

200  30 (total loss: 40/400)

210  31

220  32

230  33

240  34

250  35

.

Answer 3

The most you can tell from the given information is that he/she lost 10 lbs more than 10% his/her original weight.