Question

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 as your variable.(1 point)

Answer 1

To model the situation where both the vanilla milkshake machine and the chocolate milkshake machine will have the same amount of milkshake left, we can create an equation.

Let \( x \) represent the number of days that have passed.

For the vanilla milkshake machine:
- Capacity = 300 cups
- Sells 15 cups per day

The amount of vanilla milkshake left after \( x \) days is given by:
\[ 300 - 15x \]

For the chocolate milkshake machine:
- Capacity = 280 cups
- Sells 20 cups per day

The amount of chocolate milkshake left after \( x \) days is given by:
\[ 280 - 20x \]

To find when the two machines will have the same amount of milkshake left, we set the two expressions equal to each other:
\[ 300 - 15x = 280 - 20x \]

This is the equation that shows when the two machines will have the same amount of milkshake left.