Answer :
Final answer:
To find Jake's present weight, we set up a system of equations based on the given information. 184 pounds.
Explanation:
Let's say Jake's weight is represented by J and his sister's weight is represented by S. According to the problem, if Jake loses 8 pounds, he will weigh twice as much as his sister, which can be expressed as J - 8 = 2(S - 8).
Additionally, the sum of their current weights is 278 pounds, so we have the equation J + S = 278.
We can solve this system of equations by substitution or elimination. Let's use substitution.
From the first equation, we can rewrite it as J = 2S - 8.
Substituting this value of J into the second equation, we get (2S - 8) + S = 278.
Simplifying the equation, we have 3S - 8 = 278.
Solving for S, we find that S = 94 pounds.
Substituting this value back into the second equation, we can find J: J + 94 = 278, so J = 184 pounds.
Therefore, Jake's present weight is 184 pounds.
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