Compilation of Basic Arithmetic to Advanced Concepts

Summary:

In this hypothetical summary, we are presented with various math problems, such as algebra, age, digits, clock, geometry, motion, work, mixture, and monetary problems. Each problem is clearly defined, and the steps to find the solutions are outlined. The summary showcases the breadth of mathematical concepts, ranging from basic arithmetic to complex equations and algebraic manipulations. This collection of problems challenges the reader’s math skills and provides a comprehensive overview of mathematical problem-solving techniques.

Excerpt:

Compilation of Basic Arithmetic to Advanced Concepts

Algebra II – Worded Algebra Problems

I. Age Problems

Explanation:

• X is the present age of Person 1 (Airi).
• Y is the present age of Person 2 (Marina).
• m represents the year/s subtracted from X’s present age to determine their past age (-).
• n represents the year/s added to X’s present age to determine their future age (+).
• Since X is not equal to Y, the ages and years may differ for both individuals.

I. Age Problems – Miscellaneous

1. If X was half the age of Y m years ago:
   

   	Present	Past	Future
   X	X	X – m	X + m
   Y	Y	Y – 2m	Y + m

   Explanation:

   • X is the present age of Person X.
   • Y is the present age of Person Y.
   • m represents the number of years ago when X was half the age of Y.
   • In the past, X’s age was X – m, and Y’s was Y – 2m.
2. If X is double the age of Y in m years:
   

   	Present	Past	Future
   X	X	X – m	X + 2m
   Y	Y	Y – m	Y + m

   Explanation:

   • X is the present age of Person X.
   • Y is the present age of Person Y.
   • m represents the years added to the present age to determine the future.
   • In the future, X’s age will be X + 2m, and Y’s age will be Y + m.