Steps for Solving Algebraic Word Problems

Algebra WORD PROBLEMS Example 4: A man is 21 years older than his son. Five years ago he was four times as old as his son. How old is each now? Solution: Step 1. Let x = Son’s Age Now Step 2. Then, x + 21 = Father’s Age Now x - 5 = Son’s Age Five Years Ago (x + 21) - 5 = Father’s Age Five Years Ago Step 3. Five years ago the father was four times as old as his son. (x + 21) - 5 = 4(x - 5) Step 4. (x + 21) - 5 = 4(x - 5) x + 16 = 4x - 20 x - 4x = -20 - 16 -3x = -36 x = 12 years Solving for the other unknowns: x + 21 = 12 + 21 x + 21 = 33 years Answers: Son’s Age Now = 12 years Father’s Age Now = 33 years Step 5. The man is 21 years older than his son. 12 + 21 = 33 years Five years ago he was four times as old as his son. 33 - 5 = 28 = 4(12 - 5) = 4 x 7 Thus, the answers check. Rev. 0 Page 49 MA-02