Calculate Andrew's Final Book Cost After 30% and 10% Membership Discounts

Sequential Percentage Discounts with Compound Applications

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?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the final price of the book
00:12 Calculate each discount separately
00:23 Convert from percentages to fractions
00:41 This is the 30 percent discount
00:50 We want to calculate the book price after the discount, thus we subtract
00:57 This is the book price after the initial discount
01:04 Proceed to calculate the club member discount (10%) from the above price
01:16 Apply the same method, convert from percentages to fractions and multiply by the price
01:27 This is the discount that needs to be subtracted to determine the final price
01:34 Subtract the discount and solve to find the final 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 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?

2

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:

Price after first discount=94×(10.30)=94×0.70=65.8 dollars \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.

3

Final Answer

59.22 $

Key Points to Remember

Essential concepts to master this topic
  • Rule: Apply discounts sequentially, not simultaneously to original price
  • Technique: First discount: $94 × 0.70 = $65.80, then second discount
  • Check: Total reduction should be less than 40% of original price ✓

Common Mistakes

Avoid these frequent errors
  • Adding percentages and applying total discount to original price
    Don't add 30% + 10% = 40% and calculate $94 × 0.60 = $56.40! This ignores that the second discount applies to the already-reduced price, not the original. Always apply each discount to the current price in sequence.

Practice Quiz

Test your knowledge with interactive questions

Calculate 15% of 100:

FAQ

Everything you need to know about this question

Why can't I just add the percentages together?

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Because the second discount applies to the already reduced price, not the original price! When you get 10% off the discounted price of $65.80, you save less money than 10% of the original $94.

How do I know which discount to apply first?

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In real-world problems, apply discounts in the order they're given. Here, the store discount comes first, then the membership discount is additional.

What's the difference between my wrong answer of $56.40 and the right answer?

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Your answer of $56.40 \$56.40 assumes both discounts apply to the original price. The correct answer $59.22 \$59.22 shows the membership discount only applies to the already-reduced price of $65.80 \$65.80 .

Is there a shortcut to calculate this faster?

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Yes! Multiply the original price by both remaining percentages: $94×0.70×0.90=$59.22 \$94 \times 0.70 \times 0.90 = \$59.22 . This gives the same result as doing it step by step.

How much money did Andrew actually save?

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Andrew saved $94$59.22=$34.78 \$94 - \$59.22 = \$34.78 total. That's about 37% off the original price, which is less than the 40% you might expect from adding the discounts.

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