Math Problem Statement

Suppose your annual starting salary is $54,076. After working for a few years, you start to get yearly raises. If you get a 0.7% raise a total of 3 times and then a 1.9% raise a total of 6 times, what is your salary after all the raises?

Round your answer to the nearest dollar. Suppose the price of an item increased by 12% a total of 11 times. By what percent did the price increase in total?

Round your answer to the nearest percent (whole number). Suppose the price of an item decreased by 8% a total of 6 times. By what percent did the price decrease in total?

Round your answer to the nearest percent (whole number).

The top speed of a certain sports car is 194 miles per hour. A new unit of distance has been invented called the Zitz. Suppose that 1 mile equals 876 Zitz. What is the top speed of the car in Zitz per second?

Round your answer to the nearest tenth place.

Solution

  1. After all the raises, your salary will be $61,821.

  2. The total price increase, after increasing by 12% eleven times, is 248%.

  3. The total price decrease, after decreasing by 8% six times, is 39%.

  4. The top speed of the car is 47.2 Zitz per second.

Do you have any questions or would you like more details?

Here are 5 related questions to deepen your understanding:

  1. How would your salary change if the raise percentages or durations differed?
  2. What happens to the total percent increase when you change the percentage or the number of times the increase is applied?
  3. Can you calculate the total percent decrease if the price decreases by 10% four times?
  4. How would the Zitz per second change if 1 mile equals 900 Zitz instead of 876?
  5. What if you get an additional raise after all these increases? How would you calculate it?

Tip: Repeated percentage changes compound over time, so small changes applied multiple times can lead to significant effects.

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Math Problem Analysis

Mathematical Concepts

Compound Interest and Percentage Change
Repeated Percentage Growth
Unit Conversion
Speed and Rate Calculations

Formulas

Final Salary = Initial Salary × (1 + Raise Percentage)^Number of Raises
Final Price = Initial Price × (1 + Percentage Change)^Number of Times
Speed (Zitz per second) = Speed (miles per hour) × Zitz per mile ÷ 3600

Theorems

Compound Interest Theorem
Exponential Growth and Decay
Unit Conversion

Suitable Grade Level

Grades 10-12

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