We are given a word problem involving discounts and sales tax, and we need to find the
original price of a laptop in terms of $ p $, where $ p $ is the
total amount Alma paid, including tax.
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Step-by-step breakdown:
Let:
- $ x $ = original price of the laptop
#### 1. Apply the 20% discount:
A 20% discount means Alma pays
80% of the original price:
$$
\text{Discounted price} = 0.8x
$$
#### 2. Add 8% sales tax on the discounted price:
Sales tax is 8%, so she pays:
$$
\text{Total paid} = (1 + 0.08) \times \text{Discounted price} = 1.08 \times 0.8x = (1.08)(0.8)x
$$
But this total amount is equal to $ p $, so:
$$
p = (1.08)(0.8)x
$$
Now solve for $ x $ (the original price):
$$
x = \frac{p}{(1.08)(0.8)}
$$
Note: $ (1.08)(0.8) = 0.864 $, so:
$$
x = \frac{p}{0.864}
$$
But let’s look at the answer choices.
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Answer Choices:
A) $ 0.88p $
B) $ \frac{p}{0.88} $
C) $ (0.8)(1.08)p $
D) $ \frac{p}{(0.8)(1.08)} $
We found:
$$
x = \frac{p}{(0.8)(1.08)}
$$
So the correct answer is:
>
D) $ \frac{p}{(0.8)(1.08)} $
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✔ Final Answer: D
This represents the original price in terms of $ p $.
Parent Tip: Review the logic above to help your child master the concept of sat math worksheet.
