Algebra

Question

-3

36

1

+216

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

BRAlNBOLT Jun 22, 2024

NotThatSmart · Answer 1 · 2024-06-22T04:14:27

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! :)