Lesson HOW TO algebraize and to solve age problems?
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<H2>HOW TO algebraize and to solve age problems?</H2> In this lesson, I walk with you, giving and providing very detailed explanations on problems solutions. <H3>Problem 1</H3>After 32 years from now, a young man will be 5 times as old as he was 8 years ago. How old is the young man now? <B>Solution</B> <pre> Let x be the young man's current age. In 32 years his age will be (x+32) years. 8 years back his age was (x-8) years. The problem says that the age (x+32) years is 5 times as big as the age of (x-8) years. So, you write this equation x + 32 = 5*(x-8). Next, you simplify the equation step by step x + 32 = 5x - 40 32 + 40 = 5x - x 72 = 4x x = 72/4 = 18. <U>ANSWER</U>. The young man is 18 years old. You may check it on your own that all problem's conditions are satisfied; hence, the answer is correct. </pre> <H3>Problem 2</H3>Raymond is 12 years younger than Susan. Four years ago, she was 4 times as old as he was. Find their present ages. <B>Solution</B> <pre> Let x be the Susan age. Then the Raymond's age is (x-12), according to the condition. Four years ago, Susan was (x-4) years old. Four years ago, Raymond was ((x-12)-4) = x - 16 years old. +----------------------------------------------------------+ | "Four years ago, she was 4 times as old as he was." | +----------------------------------------------------------+ It means that x - 4 = 4*(x-16). <<<---=== it is your setup equation. You take it from the condition, using the introduced variables. Now you have this single equation and simplify it step by step x - 4 = 4x - 64 64 - 4 = 4x - x 60 = 3x x = 20. <U>ANSWER</U>. Susan is 20 years old now. Raymond is 12 years younger, i.e. 20=12 = 8 years old. </pre> <H3>Problem 3</H3>Eight years ago, Ed was ten times as old as his daughter Faith. In six years, he will be three times as old as she. What are Ed's and Faith's ages now? <B>Solution</B> <pre> Let x be the daughter's age now, and let y be the Ed's age. Eight years ago, the daughter was (x-8) years old; Ed was (y-8) years old. So, your first equation is y - 8 = 10*(x-8). (1) In six years, Ed will be (y+6) years old; his daughter will be (x+6) years old. So, your second equation is y + 6 = 3*(x+6). (2) Now our task is to solve equations (1) and (2). For it, express y from equation (1) y = 10*(x-8) + 8 = 10x - 80 + 8 = 10x - 72 (3) and substitute it into equation (2). You will get 10x - 72 + 6 = 3x + 18 10x - 3x = 18 + 72 - 6 7x = 84 x = 84/7 = 12. Thus the daughter is 12 years old now. Then the father is, according to (3), 10x - 72 = 10*12 - 72 = 120 - 72 = 48 years old. </pre> <H3>Problem 4</H3>The age of the father is twice that of the elder son. Ten years hence the age of the father will be three times that of younger son. If the difference between of ages of the two sons is 15 years, find the age of the father. <B>Solution</B> <pre> Let "x" be the present age of the elder son. Then the father's present age is 2x, while the younger son's present age is (x-15). In 10 years: The father's age will be (2x)+10 years; the younger son's age will be (x-15) + 10 = x-5 years From the other side, in ten years the age of the father will be 3(x-5) years. Thus you get an equation 2x + 10 = 3(x-5). Simplify and solve for x: 2x + 10 = 3x - 15 ---> 10 + 15 = 3x - 2x ---> x = 25. <B>Answer</B>. The elder son's present age is 25 years. The younger son's present age is 25-15 = 10 years. The father's present age is 2*25 = 50 years. </pre> My other lessons on age word problems in this site are - <A HREF=http://www.algebra.com/algebra/homework/word/age/Age-problems-and-their-solutions.lesson>Age problems and their solutions</A> - <A HREF=http://www.algebra.com/algebra/homework/word/age/Fresh-formulation-of-a-traditional-age-problem.lesson>A fresh formulation of a traditional age problem</A> - <A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson>Intricate age word problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Selected-age-word-problems-from-the-archive.lesson>Challenging age word problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problems-for-mental-solution.lesson>Age problems for mental solution</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problem-for-3-participants.lesson>Age problem for three participants</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/One-unusual-age-problem.lesson>Some unusual age word problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problems-with-a-defective-sum-of-ages.lesson>Age problems with a defective sum of ages</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Miscellaneous-age-problem.lesson>Miscellaneous age problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Entertainment-age-problems.lesson>Entertainment age problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problem-for-the-day-of-April-1.lesson>Age problem for the day of April, 1</A> - <A HREF=https://www.algebra.com/algebra/homework/word/age/04-OVERVIEW-of-lessons-on-age-problems.lesson>OVERVIEW of lessons on age problems</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-I.
