SOLUTION: Ally is 8 years older than Dan. Dan is half Ken's age. All their ages add up to 44. What are their ages?

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Question 1100601: Ally is 8 years older than Dan.
Dan is half Ken's age.
All their ages add up to 44.
What are their ages?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Ally is 8 years older than Dan.
Dan is half Ken's age.

For me, solving problems using algebra is easiest if I can set up the problem using only one variable. Perhaps another tutor will see this problem and give a response showing a solution that uses 2 or even 3 variables for the three ages. But for my solution I want to use only one variable.

One of the given pieces of information tells the relationship between Ally's age and Dan's age; the other tells the relationship between Dan's age and Ken's age.
Since both pieces of information involve Dan's age, that is the logical choice for our variable. So

let x = Dan's age
then x+8 = Ally's age
and 2x = Ken's age (Dan is half as old as Ken; so Ken is twice as old as Dan)

All their ages add up to 44.
What are their ages?

You have expressions in terms of a single variable for all three ages. Write and solve the equation that says the sum of those expressions is 44:



I assume you can finish from there....
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Ally is 8 years older than Dan.
Dan is half Ken's age.
All their ages add up to 44.
What are their ages?
~~~~~~~~~~~~~~~~~~~~ 

Sometimes (very often) when I see so simple problems, I have a wish to present the solution in such simple scheme/(form)

which will explain the solution ITSELF, without any words:


Ally  + Dan + Ken = 44

A     + D   + K   = 44


 +   + K = 44  ====> (multiply by 2 both sides)  ====>

K + 16 + K + 2K = 88

4K = 88 - 16 = 72  ====>  k =  = 18.


Answer.  Ken is 18,  Dan is half of it, i.e. 9,  Ally is 9+8 = 17.


Check.   18 + 9 + 17 = 44.   ! Correct !


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