Let's start by defining the variables:
- x: the number of days that have passed
- V: the amount of vanilla milkshake left in the machine after x days
- C: the amount of chocolate milkshake left in the machine after x days
We know that the vanilla milkshake machine starts with a capacity of 300 cups, and sells 15 cups per day. Therefore, the amount of vanilla milkshake left after x days can be expressed as:
V = 300 - 15x
Similarly, the chocolate milkshake machine starts with a capacity of 280 cups, and sells 20 cups per day. Therefore, the amount of chocolate milkshake left after x days can be expressed as:
C = 280 - 20x
We want to find the point in time when the two machines have the same amount of milkshake left. In other words, we want to find the value of x that makes V equal to C. Therefore, we can set up the following equation:
V = C
Substituting the expressions we derived earlier, we get:
300 - 15x = 280 - 20x
Simplifying and solving for x, we get:
5x = 20
x = 4
Therefore, the two machines will have the same amount of milkshake left after 4 days.
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.
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