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.
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For the vanilla milkshake machine:
- Initial capacity: 300 cups
- Sells 15 cups per day
- Amount left after \( x \) days: \[ 300 - 15x \]
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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:
- \( [_] = 300 \)
- \( [_] = 20 \)
- \( [_] = 280 \)
- \( [_] = 15 \)
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