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

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

180−20x=140−16x
; x=10

Answer 1

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

Let \( x \) represent the number of days.

For the vanilla ice cream machine:

• Initial capacity: 180 cups
• Cups sold per day: 20 cups

The amount of ice cream left after \( x \) days will be: \[ 180 - 20x \]

For the chocolate ice cream machine:

• Initial capacity: 140 cups
• Cups sold per day: 16 cups

The amount of ice cream left after \( x \) days will be: \[ 140 - 16x \]

Now, we want to find when these two amounts are equal: \[ 180 - 20x = 140 - 16x \]

Now, we can solve this equation:

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

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

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

So the solution shows that in 10 days, both machines will have the same amount of ice cream left.

Therefore, the correct response is: \[ 180 - 20x = 140 - 16x ; , x = 10 \]