Lauren was given a gift card for a coffee shop. Each morning, Lauren uses the card to buy one cup of coffee. The original amount of money on the gift card was $10 and each cup of coffee costs $2. Make a table of values and then write an equation for A, commaA, in terms of x, commax, representing the amount money remaining on the card after buying xx cups of coffee.

### Table of Values

Let's first create a table to show the amount of money remaining on the gift card after buying a certain number of cups of coffee.

| $ x $ (Number of Cups) | $ A(x) $ (Amount Remaining) |
|:------------------------:|:-----------------------------:|
| 0                        | $10                           |
| 1                        | $8                            |
| 2                        | $6                            |
| 3                        | $4                            |
| 4                        | $2                            |
| 5                        | $0                            |

### Equation for A(x)

Now, let's derive the equation for the amount of money remaining on the card, $ A(x) $, after buying $ x $ cups of coffee.

- The original amount on the card is $10.
- Each cup of coffee costs $2.

So, after buying $ x $ cups of coffee, the amount remaining on the card is:

\[
A(x) = 10 - 2x
\]

### Summary

- **Table of values** shows how the remaining balance decreases as the number of cups of coffee increases.
- **Equation**: $ A(x) = 10 - 2x $

Would you like more details or have any questions? 

### 5 Related Questions
1. How many cups of coffee can Lauren buy before the gift card runs out?
2. What happens to the value of $ A(x) $ if the price of coffee increases to $3 per cup?
3. If Lauren adds $5 to the gift card after buying 3 cups of coffee, what will the new equation for $ A(x) $ be?
4. How would the equation change if the initial amount on the gift card was $15?
5. How much money will be left after buying 7 cups of coffee?

### Tip
When writing equations for real-life situations, always identify the starting amount and the rate of change to structure the equation correctly.

Understand how to calculate the remaining amount on a gift card after buying coffee cups. Includes a table of values and an equation derivation. Suitable for grades 5-7.

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