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

Answer 1

To solve the problem, we need to set up equations based on the information provided:

1. The equation for the remaining ice cream in the vanilla machine after \( x \) days is: \[ 180 - 20x \] where 180 is the initial amount of ice cream and 20 is the amount sold per day.

2. The equation for the remaining ice cream in the chocolate machine after \( x \) days is: \[ 140 - 16x \] where 140 is the initial amount of ice cream and 16 is the amount sold per day.

We want to find the value of \( x \) when the quantities of ice cream left in both machines are equal: \[ 180 - 20x = 140 - 16x \]

Now, let's solve this equation:

1. Rearrange the equation: \[ 180 - 140 = 20x - 16x \] which simplifies to: \[ 40 = 4x \]

2. Divide both sides by 4: \[ x = 10 \]

This indicates that after 10 days, both machines will have the same amount of ice cream left.

The correct response from the provided options is: \[ 180 - 20x = 140 - 16x ; x = 10 \]