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) please

Answer 1

what is the equation

Answer 2

To find out 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 over time.

Let \(d\) represent the number of days since the ice cream was made.

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

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

We want to determine when the two amounts are equal:

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

Now, let's solve this equation for \(d\).

1. First, we can add \(20d\) to both sides:

\[
180 = 140 - 16d + 20d
\]

This simplifies to:

\[
180 = 140 + 4d
\]

2. Next, subtract 140 from both sides:

\[
180 - 140 = 4d
\]

This simplifies to:

\[
40 = 4d
\]

3. Finally, divide both sides by 4:

\[
d = 10
\]

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

To calculate the amount left in each machine after 10 days:

- **Vanilla Ice Cream**:
\[
180 - 20 \times 10 = 180 - 200 = -20 \text{ (which means it has run out)}
\]

- **Chocolate Ice Cream**:
\[
140 - 16 \times 10 = 140 - 160 = -20 \text{ (which means it has also run out)}
\]

In conclusion, both machines will run out of ice cream after 10 days, and thus at that point, they will have the same amount of ice cream left: 0 cups.

Answer 3

The equation representing when the two machines have the same amount of ice cream left is:

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

Here's what the variables and terms mean:

- \(180\) is the initial capacity of the vanilla ice cream machine.
- \(20d\) is the total amount of vanilla ice cream sold over \(d\) days.
- \(140\) is the initial capacity of the chocolate ice cream machine.
- \(16d\) is the total amount of chocolate ice cream sold over \(d\) days.

By solving the equation, we established that after 10 days, both machines would have the same amount of ice cream left, which effectively means they both reach zero at that time.