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.
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.
Sure! Let's use "x" as the number of days it takes for the two machines to have the same amount of milkshake left.
The vanilla milkshake machine starts with a capacity of 300 cups and sells 15 cups per day, so we can write the equation:
300 - 15x
The chocolate milkshake machine starts with a capacity of 280 cups and sells 20 cups per day, so we can write the equation:
280 - 20x
To find when the two machines will have the same amount of milkshake left, we set the two equations equal to each other and solve:
300 - 15x = 280 - 20x
Now, we can simplify and solve for "x":
5x = 20
x = 4
Therefore, the two machines will have the same amount of milkshake left after 4 days.
Let's use x as the number of days elapsed.
The amount of vanilla milkshake left after x days can be calculated using the formula: (300 - 15x) cups.
Similarly, the amount of chocolate milkshake left after x days can be calculated using the formula: (280 - 20x) cups.
To find when the two machines will have the same amount of milkshake left, we need to set the two equations equal to each other:
300 - 15x = 280 - 20x
Simplifying the equation:
-15x + 20x = 280 - 300
5x = -20
Dividing both sides by 5:
x = -20 / 5
x = -4
The two machines will have the same amount of milkshake left after 4 days.
To write an equation showing when the two machines will have the same amount of milkshake left, we need to equate the remaining capacity of each machine.
Let's consider x as the number of days passed.
For the vanilla milkshake machine:
The machine starts with a capacity of 300 cups, and it sells 15 cups per day. Therefore, the remaining capacity after x days would be: 300 - 15x.
For the chocolate milkshake machine:
The machine starts with a capacity of 280 cups, and it sells 20 cups per day. So, the remaining capacity after x days would be: 280 - 20x.
To find the point when both machines have the same amount of milkshake left, we equate the two expressions for remaining capacity:
300 - 15x = 280 - 20x
Now we can solve this equation to find the value of x where the two machines have the same amount of milkshake left.