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)

Question

Responses

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

180+16x=140+20x
; x=−10

Answer 1

To find when the two machines will have the same amount of ice cream left, we can start by defining \( x \) as the number of days after the ice cream is sold.

For the vanilla machine:

• Initial capacity = 180 cups
• Cups sold per day = 20 cups
• Amount of ice cream left after \( x \) days = \( 180 - 20x \)

For the chocolate machine:

• Initial capacity = 140 cups
• Cups sold per day = 16 cups
• Amount of ice cream left after \( x \) days = \( 140 - 16x \)

We want to set the amount of ice cream left for both machines equal to each other:

\[ 180 - 20x = 140 - 16x \]

Now, we can solve the equation step by step:

1. Rearranging terms: \[ 180 - 140 = 20x - 16x \]

2. Simplifying both sides: \[ 40 = 4x \]

3. Dividing both sides by 4: \[ x = 10 \]

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

The correct equation based on our setup is: \[ 180 - 20x = 140 - 16x \] And the solution gives: \[ x = 10 \]

So the answer is: 180 - 20x = 140 - 16x; x = 10.