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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
 #1
avatar+1334 
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Alright. Let's first put y in terms of x. 

We get \(y=25-x\)

 

Subbing this value back into the second equation, we get 

\(3x+75\)

 

Since x can't be negative, the smallest possible value of x is 0. 

 

When x is 0, we have \(3(0)+75=75\)

 

So 75 is our final answer. 

 

Thanks! :)

 Jun 10, 2024

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