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 z as your variable.

Answer 1

To find when the two machines will have the same amount of milkshake left, we first need to determine the remaining amount of milkshake in each machine after several days of operation.

Let's define the variable \( z \) as the number of days since the machines started making milkshakes.

**For the vanilla milkshake machine:**
- Capacity: 300 cups
- Sells: 15 cups per day
- Remaining after \( z \) days:
\[
300 - 15z
\]

**For the chocolate milkshake machine:**
- Capacity: 280 cups
- Sells: 20 cups per day
- Remaining after \( z \) days:
\[
280 - 20z
\]

Now, we want to find when the remaining amounts of milkshake in both machines are equal:
\[
300 - 15z = 280 - 20z
\]

This equation represents the scenario when both machines have the same amount of milkshake left. You can solve this equation to find the value of \( z \) (the number of days).