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
[_] - [_] × = [_] - [_x]

Answer 1

To write an equation to show when the two machines will have the same amount of milkshake left, we can first express the amount of milkshake left in each machine as a function of time, represented by the variable \( x \), where \( x \) is the number of days.

1. **For the vanilla milkshake machine:**
- Initial capacity: 300 cups
- Sells 15 cups per day
- Amount left after \( x \) days:
\[
300 - 15x
\]

2. **For the chocolate milkshake machine:**
- Initial capacity: 280 cups
- Sells 20 cups per day
- Amount left after \( x \) days:
\[
280 - 20x
\]

To find when the two machines will have the same amount of milkshake left, we can set these two expressions equal to each other:

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

This equation compares the remaining milkshake in both machines over time. Solving this will find the number of days \( x \) after which the milkshakes in both machines will be equal.

We can rearrange the terms as follows to fit your requested format:

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

This can be interpreted as:

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

Thus, you can structure your answer in the requested format:

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

So:

- \( [_] = 300 \)
- \( [_] = 20 \)
- \( [_] = 280 \)
- \( [_] = 15 \)