Age and number based linear models

1. Choose variables for the unknown ages or numbers. 2. Write the present relation. 3. Translate future or past conditions carefully. 4. Solve the pair. 5. Check whether the answer matches the story.

A small time-line table with 'present', 'after 5 years', and '5 years ago' helps avoid sign mistakes.

A common wrong answer is to add years to only one person or to both at the wrong time. The timing must match the statement exactly.

Age and number models are word problems where unknown ages or numbers are represented by variables and converted into linear equations.

Age and number models are word problems where unknown ages or numbers are represented by variables and converted into linear equations. Present age, past age, and future age are related by simple addition or subtraction of years. Digits and numbers can also be written as x and y with given conditions. If a father is 3 times as old as his son and their total age is 48, we can form linear equations and solve for each age.

These problems often involve present age, past age, future age, digits, or two numbers with a given relation. The key is to translate the statement carefully, because the algebra is usually simple once the equations are written correctly. These questions are common in exams because they test understanding of both language and equations. Present age, past age, and future age are related by simple addition or subtraction of years. Digits and numbers can also be written as x and y with given conditions. A father is 3 times as old as his son. After 12 years, he will be twice as old. Let the son’s present age be x and the father’s be 3x. Then 3x + 12 = 2(x + 12), so x = 12 and the father is 36. The exam may ask for present ages, digits of a number, or two numbers using age-related language and time change. A common wrong answer is to add years to only one person or to both at the wrong time. The timing must match the statement exactly.