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HINTS AND TO REMEMBER

Assign variables: Let x be the present age of one person.

Use algebraic expressions for past and future ages.

 

Keywords:

"Currently," "now," "present age" → x

"n years ago" → x - n

"n years from now" → x + n

Example Hint:

If "John is twice as old as Mark,"
write it as J = 2M (J = John's age, M = Mark's age).

 

Translate Word Clues into Equations

Pay attention to relationships like "twice as old," "three years older," or "half the age."

Keywords:

"Twice" → 2x

"Thrice" → 3x

"Half of" → x/2

"Sum of their ages" → x + y

"Difference of their ages" → |x - y|

Example Hint:

If "The sum of a father’s and son’s age is 50," write it as F + S = 50.

Use Substitution or Elimination to Solve for Variables

 

If two variables exist, express one in terms of the other and substitute.

Use elimination when equations are set up with addition/subtraction.

Example Hint:

If "The father is twice as old as the son, and their sum is 60,"

solve:

F=2S 

F+S=60 

Substitute F = 2S into F + S = 60 → 2S + S = 60 → 3S = 60 → S = 20.

Problem:

A mother is 30 years older than her daughter. In 5 years, the mother will be three times as old as the daughter. How old are they now?

Solution Approach:

1. Let D be the daughter's current age.

2. The mother’s current age is D + 30.

3. In 5 years: (D+30)+5 = 3(D+5) 

4. Solve for D:

D + 35 = 3D + 15

35-15 = 3D - D

20 = 2D

D=10

·  Daughter is 10 years old. ·  Mother is 40 years old.