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.(1 point)

To find out when the two ice cream machines will have the same amount of ice cream left, we can set up the following equations based on the information provided:

1. The amount of vanilla ice cream left after \( x \) days can be expressed as: \[ 180 - 20x \]

2. The amount of chocolate ice cream left after \( x \) days can be expressed as: \[ 140 - 16x \]

To find out when both amounts are equal, we can set the two expressions equal to each other: \[ 180 - 20x = 140 - 16x \]

Now, let's solve for \( x \):

1. Start by simplifying the equation: \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \]

2. Now, divide both sides by 4: \[ x = 10 \]

Thus, the solution to the equation is \( x = 10 \). This means that after 10 days, both machines will have the same amount of ice cream left.

Among the responses given, the correct equation and solution are: \[ 180−20x=140−16x ; x=10 \]