Algebraic Translations

• Translating English into algebra:
  1) Assign variables
      - Try to minimize the number of variables
      - Make use of a relationship given in the problem.
  2) Write equations
  3) Solve algebraically
  4) Evaluate the algebraic solution in the context of the problem - make sure you answer the question asked
• You can check your translations with easy numbers.
• Write an unknown percent as a variable divided by 100
• Translate bulk discounts and similar relationships carefully
• When a problem involves several quantities and multiple relationships, it is often a good idea to make a chart or a table to organize the information, i.e. age problems:
  - Put people in rows and times in columns.
  - Use variables to indicate the age of each person now, fill other columns by adding or subtracting time from the now column.
  - Write equations that relate the individuals' ages together
• In a typical Price-Quantity problem, you have two relationships:
  - the quantities sum to a total
  - the monetary values sum to a total
• Look out for hidden constraints (i.e. whole number, positive)
  - Think about what is being measured or counted and whether a hidden constraint applies.
  - To solve algebra problems that have integer constraints, test possible values systematically in a table.
  - When all quantities are positive in a problem, certain algebraic manipulations are safe to perform: 1) dropping negative solutions of equations; 2) dropping negative possibilities with inequalities (see MGMAT WT p21)