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

180−20x=140−16x
; x=20

Answer 1

To find when the two machines will have the same amount of ice cream left, we need to set up an equation based on the initial capacities and the rates at which each type of ice cream is sold.

Let's denote \( x \) as the number of days after they start selling ice cream.

For the vanilla ice cream machine:

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

For the chocolate ice cream machine:

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

We set the two expressions equal to each other to find when they have the same amount of ice cream left:

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

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

1. Rearranging the equation gives:

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

2. This simplifies to:

\[ 40 = 4x \]

3. Dividing both sides by 4:

\[ x = 10 \]

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

Thus, the correct response is:

\[ 180 - 20x = 140 - 16x; , x = 10 \]