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Word Problem - Age differences











































Brandy 28
Casey 31
Logan 3

Refer back to Week One Discussion and use the names and ages of yourself and the other two people you selected. Make sure one is older than you and one is younger than you.
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?

Comments for Word Problem - Age differences

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Apr 17, 2011
Word Problem - Age differences
by: Staff


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Part II

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

Age Difference: Brandy, current age - Logan, current age = 28 - 3 = 25 years

Brandy was 25 years old the year Logan was born.

Logan, year born: 2011 – 3 = 2008



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.


Brandy = 3*Logan

Logan = Brandy - 25


Brandy = 3*(Brandy - 25)


Logan + 25 = Brandy

Logan + 25 = 3*Logan


The final two equations are:

Brandy = 3*(Brandy - 25)

Logan + 25 = 3*Logan


Explain the reasoning which helped you develop your equation.


Three times Logan’s age must = Brandy’s age

Brandy = 3*Logan


Logan is 25 years younger than Brandy

Logan = Brandy - 25


Substitute (Brandy - 25) for Logan’s age

Brandy = 3*Logan

Brandy = 3*(Brandy - 25)


Brandy is 25 years older than Logan

Brandy = Logan + 25


Substitute (Logan + 25) for Brandy’s age

Brandy = 3*Logan

Logan + 25 = 3*Logan



Solve the equation for your ages when you are three times as old as the youngest person. Are your answers reasonable?

Brandy = 3*Brandy - 75


Brandy + 75 = 3*Brandy - 75 + 75

Brandy + 75 = 3*Brandy + 0

Brandy + 75 = 3*Brandy

Brandy - Brandy + 75 = 3*Brandy - Brandy

0 + 75 = 3Brandy - Brandy

75 = 2*Brandy

75/2 = 2*Brandy/2

75/2 = Brandy*(2/2)

75/2 = Brandy*(1)

75/2 = Brandy

37.5 = Brandy


Logan + 25 = 3*Logan

Logan - Logan + 25 = 3*Logan - Logan

0 + 25 = 3*Logan - Logan

25 = 3*Logan - Logan

25 = 2*Logan

25/2 = 2*Logan/2

25/2 = Logan*(2/2)

25/2 = Logan*(1)

25/2 = Logan

12.5 = Logan


Final Answer: Logan, age = 12.5 years; Brandy, age = 37.5 years

3*12.5 = 37.5





Thanks for writing.


Staff
www.solving-math-problems.com


Apr 17, 2011
Word Problem - Age differences
by: Staff


Part I

The question:

Brandy 28
Casey 31
Logan 3

Refer back to Week One Discussion and use the names and ages of yourself and the other two people you selected.

Make sure one is older than you and one is younger than you.

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?

The answer:


Brandy 28
Casey 31
Logan 3

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

Age Difference: Casey, current age - Brandy, current age = 31 – 28 = 3 years

Casey was 3 years old the year Brandy was born.

Brandy, year born: 2011 – 28 = 1983


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.

Brandy, age + Casey, age = 150 years

Casey, age = Brandy, age + 3

Casey, age - 3 = Brandy, age


Brandy, age + (Brandy, age + 3 years) = 150 years

Brandy, age + (Brandy, age + 3) = 150 years

2*(Brandy, age) + 3 = 150



Final equations: 2*(Brandy, age) + 3 = 150; Casey, age = Brandy, age + 3



Explain the reasoning which helped you develop your equation.

The sum of the two ages must = 150

Brandy, age + Casey, age = 150 years


Casey is 3 years older than Brandy

Casey, age = Brandy, age + 3


Substitute (Brandy, age + 3) for Casey, age

Brandy, age + (Brandy, age + 3 years) = 150 years


Combine like terms

2*(Brandy, age) + 3 = 150


Solve for your future ages. Are your answers reasonable, do they add up to 150?

2*(Brandy, age) + 3 = 150

2*(Brandy, age) + 3 - 3 = 150 - 3

2*(Brandy, age) + 0 = 150 - 3

2*(Brandy, age) = 150 – 3

2*(Brandy, age) = 147

2*(Brandy, age)/2 = 147/2

(Brandy, age)*(2/2) = 147/2

(Brandy, age)*(1) = 147/2

Brandy, age = 147/2

Brandy, age = 73.5 years

Casey, age = Brandy, age + 3

Casey, age = 73.5 years + 3

Casey, age = 76.5 years

Final Answer: Brandy, age = 73.5 years; Casey, age = 76.5 years

73.5 + 76.5 = 150

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Oct 12, 2011
help solving math problem and how and why i want to learn not just get answer
by: Anonymous

my age 33

grandpa joe's age ( the age older than me by 57 years ).

This is what I got so far:


x + (x + 57) = 150

he was 57 years old when I was born

Oct 12, 2011
help solving math problem and how and why i want to learn not just get answer
by: Anonymous

my age 33

grandpa joe's age ( the age older than me by 57 years ).

This is what I got so far:


x + (x + 57) = 150

he was 57 years old when I was born

Oct 12, 2011
Solve Equation for Age
by: Staff

my age 33

grandpa joe's age ( the age older than me by 57 years ).

This is what I got so far:


x + (x + 57) = 150

he was 57 years old when I was born

-------------------------------------------------

Your equation is correct.

x + (x + 57) = 150

Combine like terms

(x + x) + 57 = 150

(2x) + 57 = 150

2x + 57 = 150

Eliminate the 57 from the left side of the equation by subtracting 57 from both sides of the equation.

2x + 57 - 57 = 150 - 57

2x + 0 = 150 – 57

2x = 150 - 57

2x = 93

Eliminate the 2 on the left side of the equation by dividing each side of the equation by 2

2x/2 = 93/2

x*(2/2) = 93/2

x*(1) = 93/2

x = 93/2

x = 46.5

When your age is 46.5, your grandfather’s age will be 103.5

At that point the sum of your two ages will be 150



Thanks for writing.


Staff
www.solving-math-problems.com


Oct 16, 2011
solving math problems word problems and age difference
by: lynn

I need help so bad. I have been trying to solve this problem for days.

My age is 33

grandpa's age 90(who is the person older than me)

Lisa's age is: 14 (who is younger than me.

When I was born, the age of the older person =

90 – 33 = 57 years old.

Let my future age be (x) years old.
x + (x + 57) = 150
This equation has been obtained by adding my age with grandpa's age, who is older than me (by 57 years) . Since he is 57 years older than me, his age, in terms of x, will be x + 57. By simplifying the above equation, it would be presented as follows:
x + x + 57 = 150

2x + 57 = 150
By solving the equation, it would be presented as follows:
2x + 57 = 150
2x = 150 – 57
2x = ?

X = ?/2

X = ? not sure i am stuck years old.

In conclusion, my answers would be reasonable or not?.

not sure of my new age to solve this part of problem in order to equal 150

33 – 14= 19 years.

When the youngest person was born, I was 19 years old.

My age will be three times her age during that time.

The equation is x = 14(x – 19)

In the above equation, my age is represented by x. Since I am 19years older than the youngest person, her age will be x – 19.

Afterwards, the equation would be formed on the basis of the given condition.

x = 3(x – 19)

x = 3x – 57

3x – x = 57

2x = ?

x = ?/2

x = ?

My age is ? years old.

Lisa's age = 14 – ? = ?years.

In conclusion, the results are not reasonable or not?

I am aware that the future ages can not be less than the present ages.

please help



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