A dress in a shop has a marked price of D dollars. During a discount sale its price is first reduced by 15%, and then staff members receive a further 10% reduction on this already discounted price. If a staff member buys the dress, what amount does she pay, in terms of D?

Introduction / Context:
This question deals with successive percentage discounts on a marked price. It tests your understanding that successive discounts multiply as factors rather than simply adding their percentages.

Given Data / Assumptions:

• Marked price of the dress is D dollars.• First discount is 15% for the sale.• After that, staff members get a further 10% discount on the already reduced price.• We must find the final amount paid by a staff member in terms of D.

Concept / Approach:
A discount of x% leaves (1 − x/100) of the price. Successive discounts are handled by multiplying these remaining fractions. We do not add discount percentages directly because each discount is applied to a different base amount.

Step-by-Step Solution:
Step 1: After a 15% discount, the customer pays 85% of the price.Step 2: As a decimal factor, 85% = 0.85.Step 3: So sale price after first discount = 0.85D.Step 4: Staff members receive a further discount of 10% on this sale price.Step 5: After a 10% discount, the staff member pays 90% of the sale price.Step 6: Ninety percent is 0.90 as a decimal.Step 7: Final price paid = 0.90 * 0.85D.Step 8: Multiply the factors: 0.90 * 0.85 = 0.765.Step 9: So final amount paid = 0.765D.

Verification / Alternative check:
Assume D = 100 for a quick check. After 15% discount, price is 85. After another 10% discount, price is 85 * 0.90 = 76.5. As a fraction of the original 100, this is 0.765, so 0.765D is correct in general.

Why Other Options Are Wrong:
Value 0.75D corresponds to a total 25% discount, which incorrectly adds the percentages 15 and 10. Values 0.76D and 0.76D rounded forms do not reflect the correct product of the factors 0.85 and 0.90.

Common Pitfalls:
The main mistake is to add discounts directly, assuming that 15% plus 10% gives a 25% overall discount. In reality, the second discount acts on an already reduced price, so the effective discount is slightly less than 25%.

Final Answer:
The staff member pays 0.765D for the dress.