+826 Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$
+1286 Let's analyze the situation:
George usually arrives at the train station at 5:00 pm to pick up Ava.
Ava arrived early, so she started walking home an hour earlier, which means she started walking at 4:00 pm.
George and Ava met along the route between the train station and their house.
They arrived home at 4:48 pm, which means they drove for 12 minutes after picking up Ava.
Since they drove for 12 minutes after picking up Ava, Ava must have been walking for 4:48 pm - 12 minutes = 4:36 pm. Therefore, Ava had been walking for 4:36 pm - 4:00 pm = 36 minutes before George picked her up.
+1926 Alright. Let's first put y in terms of x.
We get \(y=25-x\).
Subbing this value back into the second equation, we get
. \(3x+75\)
Since x can't be negative, the smallest possible value of x is 0.
When x is 0, we have \(3(0)+75=75\)
So 75 is our final answer.
Thanks! :)
