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

Answer 1

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
page

Answer 2

Short answer

Answer 3

Choose one



140 + 16x = 180 + 20х
; x = 10
180 - 20х = 140 - 16x
; x = 20
180 - 20х = 140 - 16х
；8=10
180 + 16x = 140 + 20x
; X= -10

Answer 4

To find the number of days \( x \) after which the two machines will have the same amount of ice cream left, we can set up the following equations based on the initial capacities and daily sales.

1. **Vanilla Ice Cream Machine:**
- Initial capacity: 180 cups
- Sells 20 cups per day
- Amount of ice cream left after \( x \) days:
\[
180 - 20x
\]

2. **Chocolate Ice Cream Machine:**
- Initial capacity: 140 cups
- Sells 16 cups per day
- Amount of ice cream left after \( x \) days:
\[
140 - 16x
\]

To find when both machines have the same amount of ice cream left, we can set the two expressions equal to each other:
\[
180 - 20x = 140 - 16x
\]

Now, we will solve for \( x \).

1. Rearranging the equation:
\[
180 - 140 = 20x - 16x
\]
\[
40 = 4x
\]

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

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

To confirm, we can substitute \( x = 10 \) back into both equations to find the amount of ice cream left in each machine:

- **For the vanilla machine:**
\[
180 - 20(10) = 180 - 200 = -20 \text{ (which means it will be out of ice cream before this time)}
\]

- **For the chocolate machine:**
\[
140 - 16(10) = 140 - 160 = -20 \text{ (meaning it will also be out of ice cream)}
\]

Thus, the answer is validated by the calculation leading to \( x = 10 \) days being the point in time when both machines run out of ice cream, thereby matching their remaining amounts at zero eventually after continuous sales.

Answer 5

To determine when the two ice cream machines will have the same amount of ice cream left, we can set up equations based on the data given.

1. For the **vanilla** ice cream machine:
- Initial capacity: 180 cups
- Sells 20 cups per day
- Amount of ice cream left after \( x \) days:
\[
180 - 20x
\]

2. For the **chocolate** ice cream machine:
- Initial capacity: 140 cups
- Sells 16 cups per day
- Amount of ice cream left after \( x \) days:
\[
140 - 16x
\]

Next, we set the two amounts equal to one another to find when the two machines have the same amount of ice cream left:
\[
180 - 20x = 140 - 16x
\]

Now, we can solve for \( x \).

1. Rearrange the equation:
\[
180 - 140 = 20x - 16x
\]
\[
40 = 4x
\]

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

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

Now, let's confirm by substituting \( x = 10 \) back into both expressions to ensure they yield the same amount:
- For the vanilla machine:
\[
180 - 20(10) = 180 - 200 = -20 \text{ cups (out of stock)}
\]

- For the chocolate machine:
\[
140 - 16(10) = 140 - 160 = -20 \text{ cups (out of stock)}
\]

Since both machines will be out of ice cream at 10 days, we find that:

The correct equation from your options is:
\[
180 - 20x = 140 - 16x; \, x = 10
\]

However, since both machines run out after equal sales, we conclude \( x = 10 \) is indeed the correct answer.

Answer 6

To find when the two ice cream machines have the same amount left:

Set up the equation:
\[
180 - 20x = 140 - 16x
\]

Solve for \( x \):
\[
40 = 4x \implies x = 10
\]

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

Answer 7

The correct option is:

**180 - 20x = 140 - 16x; x = 10**

This correctly represents the situation and solves to find that after **10 days**, both machines will have the same amount of ice cream left.