Math Problem Statement

The price of an item yesterday was 

$160

. Today, the price rose to 

$232

. Find the percentage increase.

Solution

To find the percentage increase, we use the formula:

Percentage Increase=New PriceOld PriceOld Price×100\text{Percentage Increase} = \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100

In this case:

  • Old Price = 160
  • New Price = 232

Substitute these values:

Percentage Increase=232160160×100\text{Percentage Increase} = \frac{232 - 160}{160} \times 100

Calculate the difference:

232160=72232 - 160 = 72

Then,

Percentage Increase=72160×100\text{Percentage Increase} = \frac{72}{160} \times 100

Divide and multiply by 100:

Percentage Increase=0.45×100=45%\text{Percentage Increase} = 0.45 \times 100 = 45\%

Answer:

The percentage increase in price is 45%.

Would you like more details or have any questions about this calculation?

Here are five related questions for practice:

  1. If the price of another item went from $200 to $260, what would be the percentage increase?
  2. What would the percentage increase be if an item rose from $150 to $225?
  3. How would you calculate the percentage decrease if the price dropped instead of increased?
  4. If a product increased in price by 30%, what would the new price be if the original was $180?
  5. If an item’s price rises from $320 to $400, what is the percentage increase?

Tip: When calculating percentage changes, always use the original or "old" value as the base in the denominator for accuracy.

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Math Problem Analysis

Mathematical Concepts

Percentage Increase
Basic Arithmetic

Formulas

Percentage Increase = ((New Price - Old Price) / Old Price) * 100

Theorems

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Suitable Grade Level

Grades 6-8