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Equations to resolve Age Puzzle










































Write and Solve System of Equations to resolve Age Puzzle


x = younger person = 9

y = you = 36

z = older person = 52


- In years, how old was the older person when you were born?

- Write an equation that models how old in years each of you will be, when your ages add up to 150 years old.

- For example, if x = your age and the eldest person was a year older than you, you would write their age as x + 1. Then the equation would be: x + (x+1) = 150.

- Explain the reasoning which helped you develop your equation.

- Solve for your future ages.

- Are your answers reasonable, do they add up to 150?

- In years, how old were you when the youngest person was born?

- At some point during the lives of you and the youngest person, your age will be three times his/her age at that moment.

- Write an equation which models how old in years each of you will be when you are three times as old as the younger person.

- Explain the reasoning which helped you develop your equation.

- Solve the equation for your ages when you are three times as old as the youngest person.

- Are your answers reasonable?

- Respond to at least two of your classmates’ postings. Check their equations and investigate for mathematical errors. Help with a constructive critique.

Comments for Equations to resolve Age Puzzle

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Jul 25, 2012
Age Puzzle
by: Staff


The answer:


- In years, how old was the older person when you were born?

Age of older person = (older person’s current age) - (your current age)

Age of older person = z - y

Age of older person = 52 - 36

Age of older person = 16


>>> Age of older person when you were born = 16 years old



- Write an equation that models how old in years each of you will be, when your ages add up to 150 years old.

(your age) + (older person’s age) = 150

y + z = 150

the older person is 16 years older than you are, because they were 16 years old when you were born

z = y + 16

y + z = 150


y + (y + 16) = 150


>>> y + (y + 16) = 150



- Solve for your future ages.

y + (y + 16) = 150

(y + y) + 16 = 150

2y + 16 = 150

2y + 16 - 16 = 150 - 16

2y + 0 = 134

2y = 134

2y / 2 = 134 / 2

y * (2 / 2) = 134 / 2

y * (1) = 134 / 2

y = 134 / 2

y = 67


z = y + 16

z = 67 + 16

z = 83


>>> future ages: Your age (y) = 67; Older person’s age (z) = 83



- Are your answers reasonable, do they add up to 150?


The answers are reasonable and they do add up to 150.

y + z = 150

67 + 83 = 150



- In years, how old were you when the youngest person was born?

Your Age = (your current age) - (younger person’s current age)

Your Age = y - x

Your Age = 36 - 9

Your Age = 27


>>> Your Age when the youngest person was born = 27 years old



- Write an equation which models how old in years each of you will be when you are three times as old as the younger person.


y = your age
x = youngest person’s age

y = 3x

Since you will always be 27 years older than the youngest person (x):

y = x + 27

y = 3x

x + 27 = 3x


>>> x + 27 = 3x



- Solve the equation for your ages when you are three times as old as the youngest person.


x + 27 = 3x

x - x + 27 = 3x - x

0 + 27 = 3x – x

0 + 27 = 2x

2x = 27

x * (2 / 2) = 27 / 2

x * (1) = 27 / 2

x = 27 / 2

x = 13.5


y = 3x

y = 3 * 13.5

y = 40.5


>>> Ages when you are 3 times as old as the younger person: your age (y) = 40.5;
youngest person’s age (x) = 13.5


- Are your answers reasonable?


Yes, the answers are reasonable.





Thanks for writing.

Staff
www.solving-math-problems.com


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