+0  
 
-3
2
1
avatar+153 

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

 Jun 22, 2024
 #1
avatar+1230 
+1

First, let's isolate y in terms of x. We have

\(y=25-x\)

 

Now, let's subsitute this into the second equation. We have

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

 

x can't be negative, so the smallest x can be is 0. Subbing 0 in, we get

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

 

So 75 is our answer. 

 

Thanks! :)

 Jun 22, 2024

2 Online Users