Question
An electronic sensor is listed for 560.05 less 37% ,17% ,1% (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?
Solution
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AmeliaProfessional · Tutor for 6 years
Answer
**(a) Net Price Calculation:**<br /><br />* **Discount 1:** 37% of $560.05 = 0.37 * $560.05 = $207.22<br />* **Price after Discount 1:** $560.05 - $207.22 = $352.83<br />* **Discount 2:** 17% of $352.83 = 0.17 * $352.83 = $60.00 (approximately)<br />* **Price after Discount 2:** $352.83 - $60.00= $292.83<br />* **Discount 3:** 1% of $292.83 = 0.01 * $292.83 = $2.93 (approximately)<br />* **Net Price (Price after Discount 3):** $292.83 - $2.93 = $290.00 (approximately)<br /><br />Therefore, the net price is approximately **$289.90**. (The slight difference is due to rounding in intermediate steps. It's best to keep more decimal places during calculations and round only the final answer.)<br /><br /><br />**(b) Total Discount Allowed:**<br /><br />The total discount is the original list price minus the net price:<br /><br />$560.05 - $289.90 = $270.15<br /><br />Therefore, the total discount allowed is **$270.15**.<br /><br />**(c) Exact Single Rate of Discount:**<br /><br />To find the single discount rate equivalent to the series of discounts, we can use the following formula:<br /><br />Single Discount Rate = 1 - (1 - Discount 1)(1 - Discount 2)(1 - Discount 3)<br /><br />* Single Discount Rate = 1 - (1 - 0.37)(1 - 0.17)(1 - 0.01)<br />* Single Discount Rate = 1 - (0.63)(0.83)(0.99)<br />* Single Discount Rate = 1 - 0.519537<br />* Single Discount Rate = 0.480463<br /><br />Converting this to a percentage:<br /><br />0.480463 * 100% = 48.05% (approximately)<br /><br />Therefore, the exact single rate of discount is approximately **48.05%**.<br />
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