Math Problem Statement

a person income is increased 15% this year and will be 30% higher next year. if last year salary was 100000, what will it be next year?

Solution

Let's solve the problem step by step:

  1. Last year's salary was $100,000.
  2. This year's salary increased by 15%, so this year's salary is: This year’s salary=100,000×(1+0.15)=100,000×1.15=115,000\text{This year's salary} = 100,000 \times (1 + 0.15) = 100,000 \times 1.15 = 115,000
  3. Next year, the salary will be 30% higher than this year's salary, so the next year's salary is: Next year’s salary=115,000×(1+0.30)=115,000×1.30=149,500\text{Next year's salary} = 115,000 \times (1 + 0.30) = 115,000 \times 1.30 = 149,500

Thus, the salary next year will be $149,500.

Would you like further details on the calculation, or have any other questions?

Here are 5 related questions for practice:

  1. What would the salary be after a 20% increase next year?
  2. If the salary increased by 10% instead of 15% this year, what would next year’s salary be?
  3. What would the salary be in two years if it continues to increase by 15% each year?
  4. If the salary decreased by 5% next year instead of increasing by 30%, what would it be?
  5. What is the overall percentage increase in salary from last year to next year?

Tip: When calculating successive percentage increases, always apply each increase one at a time, multiplying the new salary by the respective percentage.

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Math Problem Analysis

Mathematical Concepts

Percentage Increase
Compound Percentage
Basic Arithmetic

Formulas

Current year's salary = Last year's salary × (1 + Percentage Increase This Year)
Next year's salary = This year's salary × (1 + Percentage Increase Next Year)

Theorems

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Suitable Grade Level

Grades 6-8