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

Answer 1

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 given:

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

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

We want to find the value of \(x\) when these two amounts are equal:
\[
180 - 20x = 140 - 16x
\]

Now, let's solve the equation step by step:

1. Rearrange the equation to isolate \(x\):
\[
180 - 140 = 20x - 16x
\]
\[
40 = 4x
\]

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

Thus, the correct equation is:
\[
180 - 20x = 140 - 16x
\]
And the solution is:
\[
x = 10
\]

So, the correct response is:
**180−20x=140−16x ; x=10**.