+0  
 
0
1
4
avatar+802 

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

 Sep 23, 2024
 #2
avatar+1095 
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.

 Sep 24, 2024
 #3
avatar+1858 
+1

Might have the wrong question, learnmgcat ;)

NotThatSmart  Sep 24, 2024
edited by NotThatSmart  Sep 24, 2024
 #4
avatar+1858 
+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! :)

 Sep 24, 2024
edited by NotThatSmart  Sep 24, 2024

1 Online Users