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Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

 Jun 29, 2024
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First, let's put y in terms of x to make our lives easier. 

We have

y=25x

 

Now, we subsitute it into the second expression and see what we get, 

 

We have

6x+3(25x)6x+753x3x+75

 

Now, since x must be nonegative, the smallest value it can be is 0. Thus, we have

3(0)+7575

 

So 75 is our answer. 

 

Thanks! :)

 Jun 29, 2024

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