Question

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?

Answer 1

Let \( p \) be the full price of a bag of cat food.

**Option 1: In-store deal**
- The price for one bag at full price is \( p \).
- The second bag is 40% off, which means she pays 60% of the full price for that bag:
\[
\text{Price of second bag} = 0.6p
\]
- The total cost for two bags using the in-store deal is:
\[
p + 0.6p = 1.6p
\]

**Option 2: Online purchase with a promo code**
- The cost for two bags at full price is:
\[
2p
\]
- With the promo code of $7.50 off, the total cost for the online purchase is:
\[
2p - 7.50
\]

According to Jen, these two costs are equal:
\[
1.6p = 2p - 7.50
\]

Now, let's solve for \( p \). Start by isolating terms involving \( p \):
\[
1.6p - 2p = -7.50
\]
\[
-0.4p = -7.50
\]

Next, divide both sides by -0.4:
\[
p = \frac{7.50}{0.4} = 18.75
\]

Thus, the full price of a bag of cat food is:
\[
\boxed{18.75}
\]

**Verification:**

1. **In-store deal cost calculation**:
\[
1.6p = 1.6 \times 18.75 = 30
\]

2. **Online cost calculation**:
\[
2p - 7.50 = 2 \times 18.75 - 7.50 = 37.50 - 7.50 = 30
\]

Both costs are indeed equal to $30, confirming that our solution is correct. The full price of a bag of cat food is \( \boxed{18.75} \).