AlgebraHardCost price from a markup and a discount
Algebra practice question
A shop sets its price by adding 40% to the cost of an item. During a sale, 25% is taken off the shop's price, and a customer pays $84. What was the cost of the item to the shop, in dollars?
Answer: 80
Price = 1.4c; sale price = 0.75(1.4c) = 1.05c = 84 → c = 80.
Common wrong answers
- If you answered 60
- 60 comes from 1.4c = 84, ignoring the sale.
- If you answered 112
- 112 is the shop's price before the sale (1.4 × 80).
- If you answered 73.04
- 73.04 comes from 84 ÷ 1.15, treating the two percents as a net 15%.
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