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

Sequential Percentage Discounts with Compound Reductions

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?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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?

2

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 \, \ \).

3

Final Answer

108 $

Key Points to Remember

Essential concepts to master this topic
  • Rule: Apply discounts sequentially, not all at once together
  • Technique: First discount: 150×0.80=150 × 0.80 = 120, then 120×0.90=120 × 0.90 = 108
  • Check: Total reduction is 28%, not 30%: 150150 - 108 = $42 ✓

Common Mistakes

Avoid these frequent errors
  • Adding discount percentages together
    Don't add 20% + 10% = 30% total discount! This gives 150×0.70=150 × 0.70 = 105, which is wrong. Sequential discounts compound differently because the second discount applies to the already-reduced price. Always apply each discount step-by-step to the current price.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why can't I just add the discounts together to get 30%?

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Because the second discount applies to an already reduced price! When you get 10% off the 120(nottheoriginal120 (not the original 150), you save less money than if it applied to the full price.

How do I remember the correct order of discounts?

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Apply discounts in the order given in the problem. Here, the store discount comes first, then the membership discount applies to whatever price remains.

What's the difference between 30% off once vs. 20% then 10% off?

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30% off once: Save 45,pay45, pay 105
20% then 10% off: Save 42,pay42, pay 108
Sequential discounts always save you less money than one big discount!

Is there a formula for multiple discounts?

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Yes! Multiply the remaining percentages: Final Price=Original×(1d1)×(1d2) \text{Final Price} = \text{Original} \times (1-d_1) \times (1-d_2)
So: \150 \times 0.80 \times 0.90 = \108108

How can I quickly check if my answer makes sense?

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Your final price should be between what each individual discount would give:
• 20% off alone: 120<br>10120<br>• 10% off alone: 135
Your answer (108)shouldbelessthan108) should be less than 120 ✓

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