eather and William are at their local Pokemon specialty store which is running a 20% off sale when you purchase 5 packs of cards. They are both purchasing 5 packs, and each pack costs $4.25 (taxes included). (4 points) (7.EE.2)

Question

 
(1 point)
A)   What is the original price for 5 packs of cards?  $
Question 2
Heather says she can find her cost by using the expression p - 0.2p where p is the original price for 5 packs of cards.
William says he can find his cost by using the expression (1 – 0.2)p.
(2 points)
B)   Who is correct?

Answer 1

To answer both questions, let's start with the first one.

Question 1

A) What is the original price for 5 packs of cards?

Each pack costs $4.25, and since Heather and William are purchasing 5 packs, their original price can be calculated as follows:

\[ \text{Original price} = \text{Number of packs} \times \text{Cost per pack} = 5 \times 4.25 = 21.25 \]

So the original price for 5 packs of cards is $21.25.

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Question 2

B) Who is correct regarding the expression to find their cost after the discount?

1. Heather's expression: \( p - 0.2p \)

   This expression calculates the cost after the discount by subtracting the discount (20% of the original price, \( p \)) from the original price. Specifically: \[ p - 0.2p = 0.8p \] This means she's calculating the final amount to pay after taking into account her discount (i.e., 80% of the original price).

2. William's expression: \( (1 - 0.2)p \)

   This expression also calculates the cost after the discount by multiplying the original price by \( 1 - 0.2 \) (which is the remaining 80% after the discount is applied). Specifically: \[ (1 - 0.2)p = 0.8p \]

Conclusion

Both Heather and William are correct. They are simply expressing the calculation in different forms, but both represent the same final amount to be \( 0.8p \), which accounts for a 20% discount on the original price \( p \).