Jen wants to buy two bags of food for her cat, Pumpkin. Her local grocery store has an in-store deal to buy one bag at full price and get the other for 40% off. Alternatively, she could buy two bags at full price on the store's website and use a promo code to get $7.50 off her total. After considering her options, Jen realizes the cost would be the same either way.

What is the full price of a bag of cat food?

Let's denote the full price of a bag of cat food as $ x $.

### In-store deal:
- The first bag is bought at full price: $ x $.
- The second bag is bought at 40% off: $ 0.6x $.

So, the total cost for two bags in-store is:
\[
x + 0.6x = 1.6x
\]

### Online purchase with promo code:
- Jen buys two bags at full price: $ 2x $.
- She uses a promo code to get $7.50 off.

So, the total cost for two bags online is:
\[
2x - 7.5
\]

### Equating the two costs:
Since the costs are the same, we can set the two expressions equal:
\[
1.6x = 2x - 7.5
\]

### Solving for $ x $:
1. Subtract $ 1.6x $ from both sides:
   \[
   0.4x = 7.5
   \]

2. Divide both sides by 0.4:
   \[
   x = \frac{7.5}{0.4} = 18.75
   \]

Therefore, the full price of a bag of cat food is **$18.75**.

Would you like further details or explanations?

### Related Questions:
1. How much would Jen save with the in-store deal compared to paying full price for both bags?
2. What would the total cost be if she bought three bags using the online promo code?
3. If Jen had a 20% off coupon for in-store purchases, which option would be cheaper?
4. How much would Jen pay in total if the full price of a bag increased by 10%?
5. What is the total savings percentage with the online promo code?

**Tip:** When dealing with discounts and promo codes, always express the savings in terms of the original price to make comparisons easier.

Explore how to calculate the full price of a bag of cat food with detailed steps and formulas. This problem involves understanding percentages, solving equations, and comparing discounts. Suitable for high school students.

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