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 a 140-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.
A) 180 + 16x = 140 + 20x ; x = -10
B) 180 - 20x = 140 - 16x ; x = 20
C) 140 + 16x = 180 + 20x ; x = 10
D) 180 - 20x = 140 - 16x ; x = 10
The correct equation is D) 180 - 20x = 140 - 16x ; x = 10.
To set up the equation, we need to account for the cups sold each day and the cups remaining in each machine. We subtract the number of cups sold each day from the initial capacity of each machine.
For the vanilla ice cream machine: 180 - 20x (where x is the number of days)
For the chocolate ice cream machine: 140 - 16x
To find when the two machines will have the same amount of ice cream left, we set the two expressions equal to each other:
180 - 20x = 140 - 16x
Simplifying the equation:
4x = 40
Dividing by 4:
x = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.