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.(3
Let x be the number of days it will take for the two machines to have the same amount of ice cream left.
The amount of vanilla ice cream left after x days is given by: 180 - 20x cups.
The amount of chocolate ice cream left after x days is given by: 140 - 16x cups.
Setting these two expressions equal to each other, we get:
180 - 20x = 140 - 16x
Solving for x:
180 - 140 = 16x - 20x
40 = -4x
x = -10
Since x represents the number of days, x = -10 means that the two machines will have the same amount of ice cream left 10 days before they started selling ice cream. Since this is not possible, the two machines will never have the same amount of ice cream left.