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

RedDragonl Sep 23, 2024

#2**0 **

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.

learnmgcat Sep 24, 2024

#4**+1 **

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! :)

NotThatSmart Sep 24, 2024