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1. Mother is four times as old as Mary. Five years ago, she was seven times as old. How old is each?

1. Mother is four times as old as Mary. Five years ago, she was seven times as old. How old is each?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Age problems usually follow a certain pattern. That is, they usually have certain basic facts. Frequently, they refer to ages at different points in time. For example, Ted's father's age is twice as old as Ted. This means that their ages now could be represented as: x = Ted's age now, and 2x = Ted's father's age now. Ten years ago, Ted's age was x-10, and Ted's father's age was 2x – 10. In five years or five years hence, Ted's age will be x+5 while his father's age will be 2x + 5. In tabular form, we have: Persons Past Present Future Ted х—10 x+5 Ted's Father 2х -10 2х 2.x + 5 Consider these statements Let x = John’s age now Statements Algebraic Expressions John's age now Five years more than John's age now John's sister is five years older Twice John's age two years ago Four times John’s age three years from now 1 3 4 1. Mother is four times as old as Mary. Five years ago, she was seven times as old. How old is each? 2. A man, 32 years old, has a son 8 years of age. In how many years so that the man will be twice as old as his son? 3. Three years ago, Larry was twice as old as Ben. Three years from now, Larry will be one and one-half times as old as Ben. How old is Larry? 4. In four years, Cindy's age will be the same as Tina’s age now. In two years, Tina will be twice as old as Cindy. Find the age of Cindy in three years.
Transcribed Image Text:Age problems usually follow a certain pattern. That is, they usually have certain basic facts. Frequently, they refer to ages at different points in time. For example, Ted's father's age is twice as old as Ted. This means that their ages now could be represented as: x = Ted's age now, and 2x = Ted's father's age now. Ten years ago, Ted's age was x-10, and Ted's father's age was 2x – 10. In five years or five years hence, Ted's age will be x+5 while his father's age will be 2x + 5. In tabular form, we have: Persons Past Present Future Ted х—10 x+5 Ted's Father 2х -10 2х 2.x + 5 Consider these statements Let x = John’s age now Statements Algebraic Expressions John's age now Five years more than John's age now John's sister is five years older Twice John's age two years ago Four times John’s age three years from now 1 3 4 1. Mother is four times as old as Mary. Five years ago, she was seven times as old. How old is each? 2. A man, 32 years old, has a son 8 years of age. In how many years so that the man will be twice as old as his son? 3. Three years ago, Larry was twice as old as Ben. Three years from now, Larry will be one and one-half times as old as Ben. How old is Larry? 4. In four years, Cindy's age will be the same as Tina’s age now. In two years, Tina will be twice as old as Cindy. Find the age of Cindy in three years.
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