Question

Linear Equations in Real-World Scenarios Practice
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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)

Answer 1

To model the situation, we need to express the amount of milkshake left in each machine as a function of the number of days, \( x \).

For the vanilla milkshake machine:
- It starts with 300 cups.
- It sells 15 cups per day.
- The amount left after \( x \) days can be expressed as:
\[
V(x) = 300 - 15x
\]

For the chocolate milkshake machine:
- It starts with 280 cups.
- It sells 20 cups per day.
- The amount left after \( x \) days can be expressed as:
\[
C(x) = 280 - 20x
\]

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

This equation shows the point in time when both machines will have the same amount of milkshake left.