Suppose the middle of the three consecutive integers is x then the three numbers are x - 1, x, and x + 1. Thus the greatest is x + 1 and the least is x - 1.
Can you complete the problem now?
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Pam wrote back and received two responses
If the three numbers are x, x+1 and x + 2 as you stated then the greatest is x + 2 and the least is x. Thus
Can you finish it now?
Before solving a problem, you have to understand it. A good way to understand this kind of problem is to experiment with actual numbers:
"three consecutive integers such that the greatest increased by twice the least"
Fine! take 3, 4, and 5. These are three consecutive integers. The greatest is 5; twice the least is 2*3 = 6; so the greatest increased by twice the least is 11. That's way smaller than the desired number, namely 293, but at least we know what we're doing here.
Now you try 100, 101, and 102.
We're already pretty close to 293. You should be able to guess the answer from here. But you should also be able to do it without guessing by starting with x, x+1, and x+2.
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