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# math problem

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Choose any two numbers from 150 to 350. Add 382 to both of your numbers and then divide the results by 2. What is the greatest difference that you can obtain when you subtract the two final results?

Mar 29, 2021

#1
+759
+6

so we are trying to maximize $\dfrac{382 + x}{2} - \dfrac{382 + y}{2}$, assuming $x$ is the greater number. if the set is inclusive, we have $150 \leq y \leq x \leq 350$

to maximize the difference, $x = 350$ and $y = 150.$ the fractions of each are $\dfrac{732}{2}$ and $\dfrac{532}{2}$, so the difference is $\dfrac{732-532}{2} = \dfrac{200}{2} = \boxed{100.}$

Mar 29, 2021

#1
+759
+6
so we are trying to maximize $\dfrac{382 + x}{2} - \dfrac{382 + y}{2}$, assuming $x$ is the greater number. if the set is inclusive, we have $150 \leq y \leq x \leq 350$
to maximize the difference, $x = 350$ and $y = 150.$ the fractions of each are $\dfrac{732}{2}$ and $\dfrac{532}{2}$, so the difference is $\dfrac{732-532}{2} = \dfrac{200}{2} = \boxed{100.}$