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Solving Age Problems with Linear Equations: A Step-by-Step Guide

This guide explains how to solve age problems using linear equations involving two variables. Age problems are algebraic word problems relating current, past, or future ages of individuals. Using an example with Aiza and her grandfather, we derive equations based on their ages and solve them using substitution. We demonstrate how to transform the problem into solvable equations, leading to a clear solution for the ages of both individuals. The methods emphasized include elimination, substitution, and graphing.

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Solving Age Problems with Linear Equations: A Step-by-Step Guide

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  1. Age Problem An application of Solving linear equations involving two variables

  2. Recall: There are different ways in solving linear equations involving two variables. Elimination, Substitution and Graphing are mostly used.

  3. Elimination

  4. Substitution

  5. Graphing

  6. Age Problem • Age problems are algebra word problems that deal with the ages of people currently, in the past or in the future. Example 1 The sum of Aiza’s present age and her grandfather’s present age is 68. In three years, Aiza's grandfather will be six times as old as Aiza was last year. How old is each one now?

  7. Solution (1) Representation: • We let x be Aiza’s age and y be her grandpa’s age. Equations: (1) x+y = 68 y = 68-x (2) y+3 = 6(x-1)

  8. Age Problem • Age problems are algebra word problems that deal with the ages of people currently, in the past or in the future. Example 1 The sum of Aiza’s present age and her grandfather’s present age is 68. In three years, Aiza's grandfather will be six times as old as Aiza was last year. How old is each one now?

  9. … • By Substitution, we can substitute the value of y which is 68-x to the second equation to have only one variable. • y+3 = 6(x-1) (68-x) + 3 = 6(x-1) 68-x+3 = 6x-6 71-x = 6x-6 71+6 = 6x+x 77 = 7x x =11

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