Final answer:
The single equivalent discount for the trade discount series of 5/4/1 is calculated by converting each discount to its decimal form and using the formula for successive discounts. After the calculations, the equivalent discount is approximately 0.10, or 10%, which is not one of the options provided (A-D).
Step-by-step explanation:
The single equivalent discount of the trade discount series 5/4/1 can be calculated by converting each discount to its decimal form and then combining them to find the total single discount. First, we convert each discount to decimal form: 5% becomes 0.05, 4% becomes 0.04, and 1% becomes 0.01. Next, we calculate the combined effect of applying these discounts successively by using the formula for successive discounts:
Equivalent single discount = 1 - (1 - discount1) × (1 - discount2) × (1 - discount3)
Substitute the decimal values:
Equivalent single discount = 1 - (1 - 0.05) × (1 - 0.04) × (1 - 0.01)
Equivalent single discount = 1 - (0.95 × 0.96 × 0.99)
Equivalent single discount = 1 - 0.89712
Equivalent single discount = 0.10288
When we round this to two decimal places, we get approximately 0.10, which means the correct answer to the student's question is none of the options listed (A through D). The single equivalent discount in decimal form would be approximately 0.10, or 10%.