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=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

140+16x=180+20x
; x=10
140 plus 16 x equals 180 plus 20 x ; x equals 10

180+16x=140+20x
; x=−10

Answer 1

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

1. The vanilla machine starts with 180 cups and sells 20 cups per day, so the amount of ice cream left can be expressed as:
\[
180 - 20x
\]
where \(x\) is the number of days.

2. The chocolate machine starts with 140 cups and sells 16 cups per day, so the amount of ice cream left can be expressed as:
\[
140 - 16x
\]

To find out when the two machines will have the same amount of ice cream left, we can set these two expressions equal to each other:
\[
180 - 20x = 140 - 16x
\]

Now, let's solve the equation:

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

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

Therefore, the equation to show when the two machines will have the same amount of ice cream left is:
\[
180 - 20x = 140 - 16x
\]
and the solution is:
\[
x = 10
\]

So the correct response is:
\[
180−20x=140−16x \; ; \; x=10
\]