Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$
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+75−3x3x+75
Now, since x must be nonegative, the smallest value it can be is 0. Thus, we have
3(0)+7575
So 75 is our answer.
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