Answer :
Final answer:
By solving a system of linear equations using the method of substitution, we can determine that the mom weighs 118 kg, the dad weighs 27 kg, and the son weighs 65 kg.
Explanation:
Let's assign variables to the weight of mom, dad, and son: M for mom, D for dad, and S for son.
From the given information, we can set up the following equations:
M + S = 77 (equation 1)
D + S = 92 (equation 2)
M + D = 145 (equation 3)
To solve this system of equations, we can use the method of substitution:
From equation 2, we can solve for D: D = 92 - S
Substituting this expression for D in equation 3, we have: M + (92 - S) = 145
Simplifying this equation, we get: M = S - 53
Now we can substitute this expression for M in equation 1 to solve for S: (S - 53) + S = 77
Combining like terms, we have: 2S - 53 = 77
Adding 53 to both sides, we get: 2S = 130
Dividing both sides by 2, we obtain: S = 65
Now substitute this value of S back into equation 2 to solve for D: D + 65 = 92
Subtracting 65 from both sides, we have: D = 27
Finally, substitute the values of S = 65 and D = 27 into equation 3 to solve for M: M + 27 = 145
Subtracting 27 from both sides, we get: M = 118
So, mom weighs 118 kg, dad weighs 27 kg, and son weighs 65 kg.
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