Two-Stage Discount Calculation: What Will Daniel Pay for Pants?

Question

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

Solution Steps

00:00 Calculate the final price of the pants
00:03 Calculate each discount separately
00:13 Convert percentages to fractions and multiply by the initial price
00:22 Break down 100 into factors of 20 and 5, and reduce wherever possible
00:44 This is the initial discount
00:50 Subtract this discount from the original price
00:57 This is the price after the initial discount (20%)
01:09 Proceed to calculate the club members' discount (10%)
01:16 Convert percentages to fractions and multiply by the relevant price
01:22 Break down 100 into factors of 10 and 10, and reduce wherever possible
01:32 This is the discount that needs to be subtracted to determine the final price
01:39 Subtract the discount from the price
01:42 This is the 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 $