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

• 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

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