If the problem involves a single person, then it is similar to an Integer Problem. Read the problem carefully to determine the relationship between the numbers. See example involving a single person. In these lessons, we will learn how to solve age problems that involve the ages of two or more people. In this case, using a table would be a good idea. A table will help you to organize the information and to write the equations. This is shown in the following age word problems that involve more than one person. Age Problems Involving More Than One PersonExample: Solution: Step 2: Fill in the table with information given in the question. Let x be Peter’s age now. Add 5 to get the ages in 5 yrs. Write the new relationship in an equation using the ages in 5 yrs. In 5 years, John will be three times as old as Alice. Isolate variable x Example: Solution: Step 2: Fill in the table with information given in the question. Let x be John’s age now. Add 2 to get the ages in 2 yrs. Write the new relationship in an equation using the ages in 2 yrs. In two years time, the sum of their ages will be 58. Answer: John is now 8 years old. Video Lessons - More Examples Age Word ProblemsExample: Note that this problem requires a chart to organize the information. The rows of the chart can be labeled as Mary and Son, and the columns of the chart can be labeled as “age now” and “age in 12 years”. The chart is then used to set up the equation.
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Example: Zack is four times as old as Salman. Zack is also three years older than Salman. How old is Zack?
Examples For Practise:
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problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Assume Mary's age to be x Which would mean Ann's age = 6 + x Now, Ann was Mary's age 6 yrs ago which means : x-6 And now her age is twice the age of Mary 6 yrs ago : 2(x-6) NOw, equating both the equations we get : 2(x-6) = 6 + x 2x-12 = 6 + x 2x - x = 6 + 12 x = 18 Hence, Mary's age is 18 yrs while Ann is 24 yrs old. The above question is solved by one of the experts from 24HoursTutor.com We provide live 1:1 online homework help 1. 24X7 tutors available 2. Certified tutors 3. Only for $9.99/hr One application of linear equations is what are termed age problems. When solving age problems, generally the age of two different people (or objects) both now and in the future (or past) are compared. The objective of these problems is usually to find each subject’s current age. Since there can be a lot of information in these problems, a chart can be used to help organize and solve. An example of such a table is below.
Joey is 20 years younger than Becky. In two years, Becky will be twice as old as Joey. Fill in the age problem chart, but do not solve. Using this last statement gives us the equation to solve: B + 2 = 2 ( B − 18)
Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?
Filling in the chart gives us:
The last statement gives us the equation to solve: Five years ago, the sum of their ages was 28 [latex]\begin{array}{rrrrrrrrl} (D&+&7)&+&(D&-&5)&=&28 \\ &&&&2D&+&2&=&28 \\ &&&&&-&2&&-2 \\ \hline &&&&&&2D&=&26 \\ \\ &&&&&&D&=&\dfrac{26}{2} = 13 \\ \end{array}[/latex] Therefore, Carmen is David’s age (13) + 12 years = 25 years old.
The sum of the ages of Nicole and Kristin is 32. In two years, Nicole will be three times as old as Kristin. How old are they now?
Filling in the chart gives us:
The last statement gives us the equation to solve: In two years, Nicole will be three times as old as Kristin [latex]\begin{array}{rrrrrrr} N&+&2&=&3(34&-&N) \\ N&+&2&=&102&-&3N \\ +3N&-&2&&-2&+&3N \\ \hline &&4N&=&100&& \\ \\ &&N&=&\dfrac{100}{4}&=&25 \\ \end{array}[/latex] If Nicole is 25 years old, then Kristin is 32 − 25 = 7 years old.
Louise is 26 years old. Her daughter Carmen is 4 years old. In how many years will Louise be double her daughter’s age?
Filling in the chart gives us:
The last statement gives us the equation to solve: In how many years will Louise be double her daughter’s age? [latex]\begin{array}{rrrrrrr} 26&+&x&=&2(4&+&x) \\ 26&+&x&=&8&+&2x \\ -26&-&2x&&-26&-&2x \\ \hline &&-x&=&-18&& \\ &&x&=&18&& \end{array}[/latex] In 18 years, Louise will be twice the age of her daughter. For Questions 1 to 8, write the equation(s) that define the relationship.
Solve Questions 9 to 20.
Answer Key 7.9 |