Comparing Two Store Promotions Against a Fixed Gift Card Balance
A student needs a laptop case ($48.99), a keyboard ($79.50), and a mouse ($24.99) before the term starts. Store A takes 20% off the entire order and then charges 6.5% sales tax on the discounted amount. Store B gives $10 off any order of $100 or more and then charges 5% sales tax on the discounted amount. Both stores carry identical merchandise at identical list prices. The student holds a $135 gift card that works at either store and has no other money available this month. A friend tells the student that taking 20% off and then adding 6.5% tax works out to paying 13.5% less than list price.
1. Calculate the final out-the-door total at each store.
Read the worked answer
Subtotal (identical at both stores): 48.99 + 79.50 + 24.99 = $153.48.
Store A
- Discount: 153.48 × 0.20 = 30.696, so 153.48 − 30.696 = $122.784
- Tax: 122.784 × 0.065 = $7.981
- Total ≈ $130.77
Store B
- Qualifies for the $10 credit (subtotal exceeds $100): 153.48 − 10 = $143.48
- Tax: 143.48 × 0.05 = $7.174
- Total ≈ $150.65
Store A is cheaper by about $19.88.
2. Which store can the student actually use, given the gift card? Show the comparison that decides it.
Read the worked answer
Compare each total to the $135 balance:
- Store A: $130.77 ≤ $135 → covered, leaving about $4.23 on the card.
- Store B: $150.65 > $135 → short by about $15.65, so the purchase cannot be completed there.
Store A is the only feasible option. Note that the cheaper total and the feasible option happen to coincide here, but the deciding test is the budget constraint, not the price ranking. If Store B had been cheaper but still above $135, the student would have had to choose Store A anyway.
3. Evaluate the friend's claim that the two adjustments equal 13.5% off list price.
Read the worked answer
The claim subtracts the percentages, which is invalid because the tax is applied to an already-reduced amount, not to the original price.
Multiply the factors instead: 0.80 × 1.065 = 0.852.
So the student pays 85.2% of list price, which is 14.8% less, not 13.5% less. Checked against dollars: 153.48 × 0.852 ≈ $130.77, matching the earlier total.
Why the direction differs: the discount removes 20%, and the tax then adds 6.5% of the smaller base, so the tax adds back less than 6.5% of list. Subtracting percentages is only valid when both rates apply to the same base.