Question

You earn \(10 \%\) more money at your summer job than your sister earns at her summer job. Does this mean that your sister earns \(10 \%\) less money than you? Explain your answer.

Short answer

No, the sister does not earn 10% less. A 10% increase of a certain number does not equate to a 10% decrease of the increased number.

Step-by-step solution

Understanding the problem

The student earns 10% more than the sister. Let's say the sister's earnings are $100 (a rounded number for ease of calculation). This means the student's earnings would be $110 (10% more).

Apply the concept of percentage decrease

A 10% decrease from the student's earnings of $110 would leave them with $99 (not $100). This shows that a 10% increase in one direction does not equate to a 10% decrease in the other direction.

Formulation of the conclusion

So, it can be concluded that if you earn 10% more than someone else, it does not mean that they earn 10% less than you. The percentages of increase and decrease between two numbers are not symmetrical.