A diner makes vanilla milkshakes and chocolate milkshakes. The vanilla milkshake machine has a 300-cup capacity, and sells 15 cups per day. The chocolate milkshake machine has a 280-cup capacity, and sells 20 cups per day. Write an equation to show when the two machines will have the same amount of milkshake left. Use x

To find out when the two machines will have the same amount of milkshake left, let's define \( x \) as the number of days since the milkshakes began being sold.

1. For the vanilla milkshake machine:

   • Capacity: 300 cups
   • Cups sold per day: 15 cups
   • Amount left: \( 300 - 15x \)

2. For the chocolate milkshake machine:

   • Capacity: 280 cups
   • Cups sold per day: 20 cups
   • Amount left: \( 280 - 20x \)

We want to find the value of \( x \) when the amount left in both machines is the same. Thus, we can set the two expressions equal to each other:

\[ 300 - 15x = 280 - 20x \]

This equation represents the scenario where both machines have the same amount of milkshake left.