Math Problem Statement

A person's income increased 15% this year and will be 30% higher next year. If last year's salary was 100000 what will. It be next year

Solution

To determine the salary for next year, we can break the problem into two parts: calculating this year's salary after a 15% increase, and then calculating next year's salary after a 30% increase on this year's salary.

  1. Calculate this year's salary:

    Last year's salary was $100,000\$100,000.

    This year's salary after a 15% increase: This year’s salary=100,000+(0.15×100,000)=100,000×(1+0.15)=100,000×1.15=115,000\text{This year's salary} = 100,000 + (0.15 \times 100,000) = 100,000 \times (1 + 0.15) = 100,000 \times 1.15 = 115,000

  2. Calculate next year's salary:

    This year's salary is $115,000\$115,000.

    Next year's salary after a 30% increase: Next year’s salary=115,000+(0.30×115,000)=115,000×(1+0.30)=115,000×1.30=149,500\text{Next year's salary} = 115,000 + (0.30 \times 115,000) = 115,000 \times (1 + 0.30) = 115,000 \times 1.30 = 149,500

Therefore, next year's salary will be $149,500\$149,500.

Would you like more details or have any questions?

Here are 8 relative questions that expand on this information:

  1. How do you calculate a percentage increase?
  2. What is the formula for compound interest?
  3. How would the salary change if the increase next year was only 20% instead of 30%?
  4. What if the salary increased by 10% each year for the next two years?
  5. How do you calculate a percentage decrease?
  6. What are some real-world examples where percentage increase is used?
  7. How does understanding percentages help in financial planning?
  8. What is the effect of compounding multiple percentage increases over several years?

Tip: Always double-check your calculations, especially when working with percentages, to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Percentage Increase
Compound Interest

Formulas

Percentage increase formula: New Value = Original Value × (1 + Rate)

Theorems

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Suitable Grade Level

High School