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)
25
•
140 + 16x = 180 + 20х
; x = 10
180 - 20х = 140 - 16x
; x = 20
180 - 20х = 140 - 16х
；8=10
180 + 16x = 140 + 20x
; X= -10
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Answer 1

Short answer

Answer 2

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

1. **Vanilla Ice Cream:**
- Initial amount: 180 cups
- Sells 20 cups per day
- Amount left after \(x\) days: \(180 - 20x\)

2. **Chocolate Ice Cream:**
- Initial amount: 140 cups
- Sells 16 cups per day
- Amount left after \(x\) days: \(140 - 16x\)

To find out when both machines have the same amount of ice cream left, we set the two expressions equal to each other:

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

Now, let's solve for \(x\):

1. Start by simplifying the equation:

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

2. Add \(20x\) to both sides:

\[
180 = 140 + 4x
\]

3. Subtract 140 from both sides:

\[
40 = 4x
\]

4. Divide by 4:

\[
x = 10
\]

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

Thus, the answer is \(x = 10\).

Answer 3

After 10 days, both machines will have the same amount of ice cream left.