Question

Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid oak door. If the regular price of each hollow pine door was $40, what was the total price of all 11 doors? [Official GMAT-2018]

Hint:

When calculating the total cost with discounts, first calculate the discounted price and then multiply by the quantity.

Answer 1

Step 1: Find the regular price of each solid oak door.
Let the regular price of a hollow pine door be \( P = 40 \) dollars. Since the regular price of each solid oak door is twice the price of the hollow pine door, the regular price of a solid oak door is: \[ \text{Regular price of solid oak door} = 2 \times 40 = 80 \, \text{dollars} \] Step 2: Calculate the price after the discount.
Cheryl was given a 25% discount on the regular price of each solid oak door. The price after the discount is: \[ \text{Discounted price of solid oak door} = 0.75 \times 80 = 60 \, \text{dollars} \] Step 3: Calculate the total price for 5 hollow pine doors.
The price of 5 hollow pine doors is: \[ \text{Total price of hollow pine doors} = 5 \times 40 = 200 \, \text{dollars} \] Step 4: Calculate the total price for 6 solid oak doors.
The price of 6 solid oak doors is: \[ \text{Total price of solid oak doors} = 6 \times 60 = 360 \, \text{dollars} \] Step 5: Calculate the total price of all 11 doors.
The total price of all 11 doors is the sum of the total prices of the hollow pine doors and the solid oak doors: \[ \text{Total price of all doors} = 200 + 360 = 560 \, \text{dollars} \] Step 6: Conclusion.
Thus, the total price of all 11 doors is 560 dollars.