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MAT 126 - Your age when you are three times as old as the youngest person











































Calculate your age

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

           current ages

                 Me = 54, Uncle = 81, and Niece = 18

   • Preliminary Solution

           Since 18 is the smallest number, let's start with that as "x".

           Then, the person who is 54 now is (x + 36)

           The person who is 81 now is (x + 63).

           Thus, summing, we get:

           x + (x + 36) + (x + 63) = 150.

           Or, combining like terms,

           3x + 99 = 150.

           Solving,

           3x = 51

           x = 17.


Comments for MAT 126 - Your age when you are three times as old as the youngest person

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Nov 04, 2012
Calculate your age
by: Staff


Answer


Part I


Given the ages of three people:

Me = 54 years old, Uncle = 81 years old, and Niece = 18 years old


   • Your equation and solution to determine when the sum of all three ages will equal 150 is correct:

Niece’s age + Your Age + Uncle’s age = 150


x = Your Niece’s age


x + (x + 36) + (x + 63) = 150.


Solve for future ages
      x + (x + 36) + (x + 63) = 150


Combining like terms,

3x + 99 = 150.

Solving,

3x = 51

x = 17.


x = 17


When your Niece’s age = 17 (last year)

Your Uncle’s age was = 17 + 63 = 80

Your age was = 17 + 36 = 53

then, the sum of the three ages was = 17 + 53 + 80 = 150


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

Nov 04, 2012
Calculate your age
by: Staff


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Part II

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.


Your age = 3 * (Your Niece’s age)


x = Your age


y = Your Niece’s age


x = 3 * y



Since your Niece’s age will always be 36 years younger than you


y = x - 36


Substitute x – 36 for y


x = 3 * y


x = 3 * (x - 36)


Solve for x
 x = 3 * (x - 36)


x = (3 * x) - (3 * 36)

x = 3x - 108

x + 108 = 3x - 108 + 108

x + 108 = 3x + 0

x + 108 = 3x

x + 108 - x = 3x - x

x - x + 108 = 3x – x

0 + 108 = 3x - x

108 = 3x - x

108 = 2x

2x = 108

2x / 2 = 108 / 2

x * (2 / 2) = 108 / 2

x * (1) = 108 / 2

x = 108 / 2

x = 54
(your current age)


Substitute 54 for x in the original equation


x = 3 * y


54 = 3 * y


Solve for y
54 = 3 * y


3 * y = 54

3 * y / 3 = 54 / 3

y * (3 / 3) = 54 / 3

y * (1) = 54 / 3

y = 54 / 3

y = 18




when your age = 54 (current age)

Your Niece’s age = 18 (current age)


Your Uncle’s age = 81 (current age)


Your age = 3 x your Niece’s age



Thanks for writing.

Staff
www.solving-math-problems.com



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