Use the employee discount's stated basis
The usual selling price of a T-box game console, a Kinect sensor and a game DVD is 499 dollars in total. During the Great Singapore Sale, two companies, P and Q, offered the following discounts to their customers:
| Company | T-box game console discount | Kinect sensor discount | Game DVD discount | Total price after discount |
|---|---|---|---|---|
| P | 10% | 15% | 10% | 439.15 dollars |
| Q | 5% | 25% | 20% | 426.30 dollars |
The employees from Company P are offered a further 5% discount on the original price of both the Kinect sensor and the Game DVD. Determine if this additional discount will make it more attractive for the employees to purchase all the 3 items from their own company than from Company Q. marks
[2011/AJC/Prelim/I/2]
Solution
Percentage modelling
The usual selling price of a T-box game console, a Kinect sensor and a game DVD is $499 in total. During a sale, company P discounts them by 10%, 15%, 10% (total $439.15) and company Q by 5%, 25%, 20% (total $426.30). Employees of P are offered a further 5% discount on the original price of both the Kinect sensor and the game DVD. Determine if this will make it more attractive for P's employees to buy all three items from their own company than from Q.
Hint
Let be the original prices of console, Kinect and DVD.
Three equations: the usual total, P's total, Q's total.
Then compute what an employee of P pays and compare with Q.
The extra 5% is on the original price, so it adds to the existing percentage (15% + 5% = 20%) rather than multiplying ().
The employee discount applies only to the Kinect and the DVD.
Answer · Q
No: P employees pay 426.55 dollars; Q costs 426.30 dollars.
Usual total
Original prices add up to $499.
Company P
10% off means paying 90%; 15% off means paying 85%.
Company Q
5%, 25% and 20% off mean paying 95%, 75% and 80%.
Solve
By calculator. Check: ✓.
Employee price at P
The extra 5% is taken off the original price: Kinect off, DVD off. The console keeps its 10% discount.
Compare
An employee still pays 25 cents more at P than a customer at Q.
Explore the idea