Linear Equations in Real-World Scenarios Practice

Question

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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)
Remaining Attempts : 3

Answer 1

To find the point at which both the vanilla and chocolate milkshake machines will have the same amount of milkshake left, we can set up two equations based on the information provided.

Let \( x \) be the number of days.

For the vanilla milkshake machine:

• Initial capacity: 300 cups
• Sells 15 cups per day

The equation for the amount of vanilla milkshake left after \( x \) days is: \[ V(x) = 300 - 15x \]

For the chocolate milkshake machine:

• Initial capacity: 280 cups
• Sells 20 cups per day

The equation for the amount of chocolate milkshake left after \( x \) days is: \[ C(x) = 280 - 20x \]

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

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