Help - Math - Ages add up to 150

by Pat
(Fayetteville)

Given the ages of three people:

6 years old, 47 years old, 68 years old

   • Write an equation:

       1. 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. )

       2. Explain the reasoning which helped you develop your equation.

       3. 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?

   • Write an equation:

       1. which models how old in years each of you will be when you are three times as old as the younger person.
(At some point during the lives of you and the youngest person, your age will be three times his/her age at that moment.)

       2. Explain the reasoning which helped you develop your equation.

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

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Jul 31, 2012

Ages add up to 150
by: Staff

Answer:

Given the ages of three people:

6 years old, 47 years old, 68 years old

• Write an equation:

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

The oldest person is now 68 years old. That person is exactly 21 years older than the middle person.

Middle person’s age + Older person’s age = 150

x = middle person’s age

x + (x+21) = 150

Explain the reasoning which helped you develop your equation.

Middle person’s age + the age of someone 21 years older = 150

x + (x + 21) = 150

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

x + (x + 21) = 150

(x + x) + 21 = 150

2x + 21 = 150

2x + 21 - 21 = 150 - 21

2x + 0 = 150 - 21

2x = 150 - 21

2x = 129

2x/2 = 129/2

x*(2/2) = 129/2

x*(1) = 129/2

x = 129/2

x = 64.5

when the middle person’s age = 64.5
and the older person’s age = 64.5 + 21 = 85.5

then, the sum of your two ages will = 64.5 + 85.5 = 150

how old was the middle person when the youngest person was born?

Your age now = middle person’s age now – younger person’s age now

= 47 - 6

Middle person’s age when younger person born = 41

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.

x = middle person’s age
y = youngest person’s age

x = 3y

Since the youngest person was born when the middle person was 41, the younger person will always be 41 years younger:

y = x - 41

x = 3(x - 41)

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

x = 3(x - 41)

x = 3*x - 3*41

x = 3x - 3*41

x = 3x - 123

x - x = 3x - x - 123

0 = 3x - x - 123

0 = 2x - 123

0 + 123 = 2x - 123 + 123

102 = 2x - 123 + 123

123 = 2x + 0

123 = 2x

123/2 = 2x/2

61.5= 2x/2

61.5= x*(2/2)

61.5= x*(1)

61.5 = x

x = 61.5

y = x - 41

y = 61.5 - 41

y = 20.5

When the middle person is 61.5, the younger person will be 20.5 years old (61.5-41=20.5).

At that point in time, the middle person’s age will be exactly 3 times the younger person’s age:

3 * 20.5 = 61.5

Thanks for writing.

Staff
www.solving-math-problems.com

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Help - Math - Ages add up to 150

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