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

learnmgcat Jun 29, 2024

#1**+1 **

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

We have

\(y=25-x\)

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

We have

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

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

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

So 75 is our answer.

Thanks! :)

NotThatSmart Jun 29, 2024