This question can be solved with fairly straight-forward Algebra (as the other solutions have proven). It can also be solved by TESTing THE ANSWERS and a bit of logic.
We're told that the total weight of Jake and his sister is 278 pounds. We're also told that if Jake lost 8 pounds, then he would weight TWICE as much as his sister. This means that, right now, Jake weighs MORE than TWICE his sister. We're asked for Jake's current weight.
Since Jake weighs more than twice his sister, his weight is MORE than 2/3 of the 278 pounds. Looking at these answer choices, I would TEST one of the bigger values first... Under normal circumstances, that would be Answer D. With a quick estimate though we can see that 2/3 of 270 pounds would be 180 pounds, but Jake has to weight MORE than that, so I'm going to TEST Answer E first....
If Jake weights 188 pounds...
Jake - 8 = 180 pounds....
Sister = 90 pounds
90 + 180 + 8 = 278 pounds
This is a MATCH for the information in the prompt, so Jake MUST weight 188 pounds.
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