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

 Sep 29, 2024
 #1
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we get 3x+3y=75. since we need to add 3x, we just make x=0, since the questions says "nonnegative". therefore, the minimum value is 75.

 Sep 29, 2024
 #2
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If we multiply both sides by 3, we get 3x+3y=75 . We notice that 6x+3y is 3x more than 3x+3y. If x is 0, then 3x is 0. 75 + 0 = 75, so the minumum value of 6x+3y is 75.

 Sep 30, 2024

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