SOLUTION: Hi. I'm not sure how to set up the equation: A father is 43 and he has two kids who are 9 and 11. How many years have to go by so that the ages of the two kids equal the age of th

Question 1110355: Hi. I'm not sure how to set up the equation:
A father is 43 and he has two kids who are 9 and 11. How many years have to go by so that the ages of the two kids equal the age of the father?
I think it's:
9 + x + 11 + x = 43
20 + 2x = 43
2x = 43
But it doesn't seem to make sense to have a decimal age for x.
Found 4 solutions by rothauserc, KMST, ankor@dixie-net.com, ikleyn:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
(9+x) + (11+x) = (43+x)
:
2x +20 = 43 +x
:
x = 23
:
in 23 years the father will be 66 and his sons will be 32 and 34
:

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
The wording you posted does not talk about the sum of the ages of the two kids.
Did you mean "ages" or "sum of the ages" of the two kids?

Each of the two kids will be 43 years old someday (unless one or both die at a younger age).
That would give you two different equations,
and , with two different results.
Of course, at no time will the father and a child be the same age.

The sum of the ages of the two kids will always be an even number,
so the sum will never be 43.
However, as all 3 of them age by years,
the sum of the two children's ages will be the age of the father when
.
That may be the intended problem and equation.

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
A father is 43 and he has two kids who are 9 and 11.
How many years have to go by so that the ages of the two kids equal the age of the father?
:
let y = no. of years for this to be true
43 + y = (y+9) + (y+11)
43 + y = 2y + 20
43 - 20 = 2y - y
23 = y
:
23 yrs for this to be true
:
:
Check this:
43 + 23 = 9 + 23 + 11 + 23
66 = 32 + 34
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution
in this site.

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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