A garden set is listed for $616.79 less 41 %, 18 %, 3 %. (a) What is the net price? (b) What is the total amount of discount allowed? (c) What is the exact single rate of discount that was allowed?
The correct answer and explanation is:
(a) Net Price Calculation
To find the net price, we need to calculate the price after all the discounts have been applied one after another. The garden set’s original price is $616.79, and the discounts are 41%, 18%, and 3%.
The formula to find the price after applying successive discounts is as follows:
- First, calculate the price after the first discount (41%): 616.79×(1−0.41)=616.79×0.59=364.60616.79 \times (1 – 0.41) = 616.79 \times 0.59 = 364.60
- Then, apply the second discount (18%) on the new price: 364.60×(1−0.18)=364.60×0.82=299.17364.60 \times (1 – 0.18) = 364.60 \times 0.82 = 299.17
- Finally, apply the third discount (3%) on the new price: 299.17×(1−0.03)=299.17×0.97=290.61299.17 \times (1 – 0.03) = 299.17 \times 0.97 = 290.61
So, the net price is $290.61.
(b) Total Amount of Discount Allowed
To calculate the total amount of discount allowed, subtract the net price from the original price: 616.79−290.61=326.18616.79 – 290.61 = 326.18
Thus, the total amount of discount allowed is $326.18.
(c) Exact Single Rate of Discount
The single equivalent rate of discount can be found by considering the overall percentage reduction from the original price to the final net price. To do this, use the formula: Single Rate of Discount=1−Net PriceOriginal Price\text{Single Rate of Discount} = 1 – \frac{\text{Net Price}}{\text{Original Price}}
Substituting the values: Single Rate of Discount=1−290.61616.79=1−0.471=0.529\text{Single Rate of Discount} = 1 – \frac{290.61}{616.79} = 1 – 0.471 = 0.529
Converting this to a percentage: 0.529×100=52.9%0.529 \times 100 = 52.9\%
Thus, the exact single rate of discount is 52.9%.
Summary:
- Net Price: $290.61
- Total Amount of Discount: $326.18
- Exact Single Rate of Discount: 52.9%