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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 10, 2024
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Our first step is to isolate y from the first equation. Moving x to the other side, we get

\(y=25-x\)

 

Now, we plug this value of y into the second equation. We get

\(6x+3(25-x)\\ 6x+75-3x\\ 3x+75\)

 

Now, x has to be nonegative, so it cannot be a negative number. The next smallest number is 0. 

 

Plugging in the value of 0, we get

\(3(0)+75\\ 75\)

 

So 75 is our final answer!

 

Thanks! :)

 Jun 10, 2024

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