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# help

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If $$\lfloor x \rfloor = 4,$$ find the sum of all possible values of $$\lfloor 4x \rfloor.$$

May 9, 2019

#1
+115
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Another way of writing $$\lfloor x\rfloor = 4$$ defines x values in the interval of $$4 \leq x < 5$$

If we multiply this interval by 4, we have that $$16\leq 4x < 20$$.

In order to get the sum, we have to acknowledge that our 4x is still being floored, given $$\lfloor 4x \rfloor$$. Therefore, only integer values within the interval can be a result of this. For example, $$x = 4.625$$ satisfies that $$\lfloor x \rfloor = 4$$. Then, $$\lfloor 4x \rfloor = \lfloor 4*4.625\rfloor = \lfloor 18.5 \rfloor = 18$$

The integers within $$[16, 20)$$ are 16, 17, 18, and 19. $$16+17+18+19= 70$$.

If $$\lfloor x \rfloor = 4,$$ the sum of all possible values of $$\lfloor 4x \rfloor$$ is $$70$$.

May 9, 2019
#2
+8724
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Hey, that's a good way to do it!

hectictar  May 9, 2019