Examples with solutions for Quantity, percentage, percentage value: Two changes in percentages

Exercise #1

In a bookstore there is a 30% discount on all books. Customers with a membership are entitled to an additional 10% discount. Andrew has a membership and wants to buy a book that costs 94 dollars. What will the discounted price of the book be?

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the price after the first discount.
  • Step 2: Calculate the price after the additional membership discount.

Now, let's work through each step:

Step 1: Apply the first discount of 30% to the original price of 94.
The price after a 30% discount is calculated as follows:

\( \text{Price after first discount} = 94 \times (1 - 0.30) = 94 \times 0.70 = 65.8 \text{ dollars}

Step 2: Apply the additional membership discount of 10% to the new price.
The final price after the additional 10% discount is calculated as follows:

Final discounted price=65.8×(10.10)=65.8×0.90=59.22 dollars \text{Final discounted price} = 65.8 \times (1 - 0.10) = 65.8 \times 0.90 = 59.22 \text{ dollars}

Therefore, the discounted price Andrew will pay is 59.22 59.22 dollars.

Answer

59.22 $

Exercise #2

In a clothing store there is a - 20% discount on all pants in the store. For customers with a membership there is a further 10% discount. Daniel wants to buy a pair of pants and has a membership card, the cost of the pants is 150 $: How much will Daniel need to pay in total?

Video Solution

Step-by-Step Solution

To solve this problem, we'll sequentially apply the discounts.

  • Step 1: Calculate the store discount (20% off).

  • Step 2: Apply the membership discount (additional 10% off) on the reduced price.

Let's calculate:

Step 1: The store discount is 20%, so the price after the store discount is:

\text{Price after 20\% discount} = \150 \times (1 - 0.20) \)

\text{Price after 20\% discount} = \150 \times 0.80 = \120120

Step 2: With the membership card, Daniel gets an extra 10% discount on the already reduced price of \( \120120 .

\text{Price after additional 10\% discount} = \120 \times (1 - 0.10) \)

\text{Price after additional 10\% discount} = \120 \times 0.90 = \108108

Therefore, the total amount Daniel needs to pay is \108 \).

Hence, the correct choice is 2 2 : 108 \, \ \).

Answer

108 $