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

**In-store deal:**
1. Jen buys one bag at full price: \( p \).
2. She buys the second bag at 40% off, which costs \( 0.6p \).

So, the total cost when buying in-store is:
\[
p + 0.6p = 1.6p
\]

**Online deal:**
1. Jen buys two bags at full price, costing \( 2p \).
2. After using the promo code, she gets $7.50 off, leading to a total cost of:
\[
2p - 7.50
\]

**Setting the costs equal:**
Since Jen realizes the costs are the same, we can set the two expressions equal to each other:
\[
1.6p = 2p - 7.50
\]

**Solving for \( p \):**
1. Rearranging the equation gives:
\[
2p - 1.6p = 7.50
\]
\[
0.4p = 7.50
\]
2. Dividing both sides by 0.4 gives:
\[
p = \frac{7.50}{0.4} = 18.75
\]

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