Question

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) Responses 180−20x=140−16x ; x=20 180 minus 20 x equals 140 minus 16 x ; x equals 20 180+16x=140+20x ; x=−10 180 plus 16 x equals 140 plus 20 x ; x equals negative 10 140+16x=180+20x ; x=10 140 plus 16 x equals 180 plus 20 x ; x equals 10 180−20x=140−16x ; x=10

Answer 1

To find out when the two ice cream machines will have the same amount of ice cream left, we can use the following equations based on their capacities and daily sales.

Let \( x \) be the number of days after which we want to find out when they will have the same amount of ice cream left.

1. For the vanilla ice cream machine: \[ \text{Amount left} = 180 - 20x \]

2. For the chocolate ice cream machine: \[ \text{Amount left} = 140 - 16x \]

We need to set these two expressions equal to each other: \[ 180 - 20x = 140 - 16x \]

Now, let's solve this equation:

1. Start by isolating \( x \): \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \] \[ x = 10 \]

So, the two machines will have the same amount of ice cream left after 10 days.

The correct response is: \[ 180 - 20x = 140 - 16x; \quad x = 10 \]