an ice cream shop makes vanilla and chocolate ice cream. the vanilla 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 an equation to show when the two machines will have the same amount of ice cream left.

Question

a. 140+16x=180+20x ; x = 10
b. 180-20x=140-16x ; x = 10
c. 180-20x = 140-20x ; x = -10
d. 180-20x=140-16x ; x = 20

Answer 1

To find when the two machines will have the same amount of ice cream left, we can express the amount of ice cream left in each machine after \( x \) days.

For the vanilla ice cream machine:

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

For the chocolate ice cream machine:

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

We want to find the point in time (after \( x \) days) when both machines have the same amount left, so we set the two expressions equal to each other:

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

This matches option d from your list:

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

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

1. Rearranging gives: \[ 180 - 140 = 20x - 16x \]
2. Simplifying further: \[ 40 = 4x \]
3. Therefore: \[ x = 10 \]

So, the correct choice is d: \( 180 - 20x = 140 - 16x; x = 10 \) (though there is a correction needed in labeling the choice; it indeed leads to \( x = 10 \)).

Answer 2

are you sure

Answer 3

Let me clarify the setup one more time to confirm:

1. The vanilla ice cream machine starts with 180 cups and sells 20 cups per day. After \( x \) days, the amount of vanilla left is given by the equation: \[ 180 - 20x \]

2. The chocolate ice cream machine starts with 140 cups and sells 16 cups per day. After \( x \) days, the amount of chocolate left is given by the equation: \[ 140 - 16x \]

We want to find when the amount left in both machines is the same, which gives us the equation: \[ 180 - 20x = 140 - 16x \]

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

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

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

Thus, after 10 days, both machines will have the same amount of ice cream left. Therefore, the correct equation to describe this scenario is: \[ 180 - 20x = 140 - 16x \]

The correct choice from the given options is indeed: d. \( 180 - 20x = 140 - 16x; x = 10 \)

Thanks for your patience, and I can confirm this calculation is correct.