An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180 cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has 150 cup capacity and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left
Let's assume the number of days it takes for the two machines to have the same amount of ice cream left is represented as "d".
For the vanilla ice cream machine:
The initial amount of vanilla ice cream in the machine is 180 cups.
It sells 20 cups per day.
Therefore, the amount of vanilla ice cream left after "d" days is 180 - 20d.
For the chocolate ice cream machine:
The initial amount of chocolate ice cream in the machine is 150 cups.
It sells 16 cups per day.
Therefore, the amount of chocolate ice cream left after "d" days is 150 - 16d.
To find when the two machines will have the same amount of ice cream left:
180 - 20d = 150 - 16d
Simplifying the equation:
180 - 150 = -16d + 20d
30 = 4d
Dividing both sides by 4:
30/4 = d
7.5 = d
Therefore, it will take 7.5 days for the two machines to have the same amount of ice cream left.
Let's denote the number of days as 'x.'
The amount of vanilla ice cream left after 'x' days can be calculated by subtracting the number of cups sold per day from the initial capacity: 180 - 20x.
Similarly, the amount of chocolate ice cream left after 'x' days can be calculated by subtracting the number of cups sold per day from the initial capacity: 150 - 16x.
To find when the two machines will have the same amount of ice cream left, we can equate the two expressions:
180 - 20x = 150 - 16x.
Simplifying the equation, we have:
4x = 30.
Dividing both sides by 4, we get:
x = 7.5.
Therefore, the two machines will have the same amount of ice cream left after 7.5 days.