We are told:
- Alma bought a laptop with a
20% discount off the
original price.
- She paid
p dollars total, which includes an
8% sales tax on the
discounted price.
- We need to find the
original price in terms of
p.
---
Step 1: Define variables
Let the
original price be
x dollars.
After a
20% discount, the
discounted price is:
>
0.80x
Then, an
8% sales tax is applied to this discounted price. So the
total amount paid (which is p) is:
>
p = (discounted price) × (1 + tax rate)
>
p = 0.80x × 1.08
---
Step 2: Solve for x (original price)
We have:
>
p = 0.80 × 1.08 × x
So,
>
x = p / (0.80 × 1.08)
---
Step 3: Match with answer choices
Looking at the options:
A) 0.88p → Incorrect
B) p / 0.88 → Incorrect (this would be if it were 12% discount or something else)
C) (0.8)(1.08)p → This is multiplying p by 0.8×1.08, but we need to *divide* p by that → Incorrect
D)
p / [(0.8)(1.08)] →
Exactly what we got!
---
✔ Final Answer: D) $\frac{p}{(0.8)(1.08)}$
This represents the original price of the computer in terms of p.
Parent Tip: Review the logic above to help your child master the concept of sat math practice worksheet.
