Calculate the New Shirt Price: $160 with a 30% Discount

Percentage Discounts with Dollar Calculations

The price of a shirt in a shop is $160. After one month, the shop offered a 30% discount on their shirts. Calculate the price of the shirt after the discount.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the reduced price of the shirt
00:05 Convert the percentage to a fraction
00:12 Use the formula to convert percentages to fractions
00:20 Apply this formula to our exercise
00:27 Multiply this fraction by the original price in order to determine the discount
00:42 Factor 30 into 3 and 10, and 100 into 10 and 10
00:47 Factor 160 into 16 and 10
00:57 Simplify wherever possible
01:07 This is the discount
01:17 Now subtract the discount from the original price in order to determine the new price
01:22 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The price of a shirt in a shop is $160. After one month, the shop offered a 30% discount on their shirts. Calculate the price of the shirt after the discount.

2

Step-by-step solution

To solve the problem of finding the price of a shirt after a 30% discount, let's follow these clear steps:

  • Step 1: Determine the discount amount using the formula: Discount Amount=Original Price×(Discount Percentage100) \text{Discount Amount} = \text{Original Price} \times \left(\frac{\text{Discount Percentage}}{100}\right) .
  • Step 2: Calculate the price after discount: Price after Discount=Original PriceDiscount Amount \text{Price after Discount} = \text{Original Price} - \text{Discount Amount} .
  • Step 3: Verify this process with the problem requirements and check the options if provided.

Now, let's apply these steps:

Step 1: Calculate the discount amount:

The original price of the shirt is 160, and the discount percentage is 30%.

Using the formula, the discount amount is \( 160 \times \left(\frac{30}{100}\right) = 48 dollars.

Step 2: Find the final price after applying the discount:

The price after the discount becomes 16048=112 160 - 48 = 112 dollars.

Thus, the price of the shirt after applying the 30% discount is \112 \).

3

Final Answer

$112

Key Points to Remember

Essential concepts to master this topic
  • Formula: Discount Amount = Original Price × (Percentage ÷ 100)
  • Technique: Calculate 160×30100=48 160 \times \frac{30}{100} = 48 then subtract from original
  • Check: Final price should be less than original: 112<112 < 160 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing discount amount with final price
    Don't think the 30% discount of 48isthefinalprice=wronganswerof48 is the final price = wrong answer of 48! The discount amount is what you subtract, not what you pay. Always subtract the discount from the original price to get the final cost.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

\( \frac{2}{100}=\text{?} \)

FAQ

Everything you need to know about this question

Why do I divide the percentage by 100?

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Percentages are parts of 100! When you see 30%, it means 30 out of 100, or 30100 \frac{30}{100} . Dividing by 100 converts the percentage to a decimal (0.30) that you can multiply with.

Can I calculate the final price directly without finding the discount amount?

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Yes! Since a 30% discount means you pay 70% of the original price, you can calculate: 160×0.70=112 160 \times 0.70 = 112 . This shortcut works because 100% - 30% = 70%.

What if the discount percentage is a decimal like 12.5%?

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The process stays the same! Convert to decimal: 12.5100=0.125 \frac{12.5}{100} = 0.125 . Then multiply: Original Price × 0.125 = Discount Amount. Always divide any percentage by 100 first.

How do I know if my final answer makes sense?

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Check these three things:

  • Final price is less than the original price
  • The discount amount is reasonable (not too big or small)
  • When you add discount + final price, you get the original price

Why can't I just subtract 30 from 160?

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Because 30% doesn't mean 30!The<strong>30! The <strong>%</strong> symbol means "per hundred," so 30% of 160 is much larger than $30. You must calculate what 30% actually equals in dollars first.

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