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

Answer 1

To determine when the two machines will have the same amount of ice cream left, we can set up the equations based on their capacities and the rates at which they sell ice cream.

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

1. The vanilla ice cream machine starts with 180 cups and sells 20 cups per day: \[ \text{Remaining vanilla after } x \text{ days} = 180 - 20x \]

2. The chocolate ice cream machine starts with 140 cups and sells 16 cups per day: \[ \text{Remaining chocolate after } x \text{ days} = 140 - 16x \]

We set these two expressions equal to each other to find when they have the same amount of ice cream left: \[ 180 - 20x = 140 - 16x \]

Now, we will solve for \( x \).

First, rearranging the equation gives: \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \]

Next, divide both sides by 4: \[ x = 10 \]

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

The correct response to your original question is: 180 - 20x = 140 - 16x ; x = 10.