Answer :
Final answer:
Sandra's weight alone is determined by using the given combined weights of pairs and the total combined weight to solve a set of linear equations. Sandra weighs 110 pounds when isolated from the group's weight.
Explanation:
The question involves solving for the weight of an individual when given the combined weights of different pairs and the total weight of all three individuals. Let's denote Sandra's weight as S, Peter's weight as P, and Martin's weight as M. Using the given information:
- S + P = 275 pounds
- S + M = 245 pounds
- S + P + M = 410 pounds
To find Sandra's weight alone, we can substitute the first equation into the third equation:
(1) S + P = 275
(3) S + P + M = 410
Subtract (1) from (3): M = 410 - 275 = 135 pounds.
Next, we substitute the value of M into the second equation to find S:
(2) S + M = 245 pounds
S + 135 pounds = 245 pounds
Therefore, Sandra weighs alone: S = 245 - 135 = 110 pounds.
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