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

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

180−20x=140−16x
; x=10

Answer 1

To find out when the two ice cream machines will have the same amount of ice cream left, we need to set up equations for the amount of ice cream left in each machine after \( x \) days.

For the vanilla machine:

• Initial capacity: 180 cups
• Sells: 20 cups per day
• Ice cream left after \( x \) days: \( 180 - 20x \)

For the chocolate machine:

• Initial capacity: 140 cups
• Sells: 16 cups per day
• Ice cream left after \( x \) days: \( 140 - 16x \)

We want to find \( x \) when both machines have the same amount of ice cream left:

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

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

1. Add \( 20x \) to both sides: \[ 180 = 140 - 16x + 20x \] \[ 180 = 140 + 4x \]

2. Subtract 140 from both sides: \[ 180 - 140 = 4x \] \[ 40 = 4x \]

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

So, the correct equation and solution is: \[ 180 - 20x = 140 - 16x \] and \( x = 10 \).

This solution aligns with the option:

180−20x=140−16x ; x=10.