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:
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?
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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 !
