SOLUTION: Jon is 4 years younger than Kate. Millie is three times as old as Kate . If the sum of their ages is 76, how old are they

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Question 1061429: Jon is 4 years younger than Kate. Millie is three times as old as Kate . If the sum of their ages is 76, how old are they
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Ages are j, k, m.




Substitute for j and for m, in the age-sum equation...




Do the rest....
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Jon is 4 years younger than Kate. Millie is three times as old as Kate . If the sum of their ages is 76, how old are they
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let K be Kate's present age.

Then Jon's age is K-4 years, Millie's age is 3K years.

The sum of their ages is K + (K-4) + 3K, and it is 76 years.
It gives you an equation

K + (K-4) + 3K = 76.


Simplify and solve for K:

5K - 4 = 76,

5K = 76 + 4,

5K = 80  --->  K =  = 16.

So, Kate is 16 years old.

Hence, Jon is K-4 = 16-4 = 12; Millie is 3K = 3*16 = 48 years old.

Anwer.  Kate is 16 years old.  Jon is 12 years old.  Millie is 48 years old.

Solved.

From the solution, learn on how to choose the major unknown; how to express other unknowns and how to make an equation for the problem.

Surely, this problem is not about writing the system of three equations in three unknowns.
It is about reducing the problem to one equation in one single unknown from the very beginning.



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