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Question 1121307: I was asked to solve this linear equation.
A man is four times as old as his son. In four years time he will be three times older in age, what are their ages now
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the son's age now.
the father's age now is therefore equal to 4x.
i think you mean that, in 4 years time, he will be 3 times as old as his son.
in 4 years, the father will be 4x + 4 years old.
in 4 years, the son will be x + 4 years old.
in 4 years the father will be 3 times as old as the son leads to the equation:
4x + 4 = 3 * (x + 4)
simplify this to get 4x + 4 = 3x + 12
subtract 3x from both sides of this equation and subtract 4 from both sides of this equation to get:
x = 8
that's his son's age today.
he is 4 * 8 = 32 years old today.
in 4 years, he will be 36 years old and his son will be 12 years old.
36 = 3 * 12 means that he will be 3 times as old as his son in 4 years.
today he's 32 and his son is 8.
32 = 4 * 8
4 years from now, he will be 36 and his son will be 12.
36 = 3 * 12.
your solution is that their he is now 32 and his son is now 8.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
I was asked to solve this linear equation.
A man is four times as old as his son. In four years time he will be three times older in age, what are their ages now
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1. Hey ! It is not a linear equation !
It is age word problem, instead.
2. Your formulation in the post is FATALLY WRONG.
The correct formulation is THIS :
A man is four times as old as his son. In four years  he will be three times  as old as his son.
What are their ages now ?
Solution
x = 4y (x= the father age; y = the son age)
x + 4 = 3*(y+4) (in 4 years . . . )
4y + 4 = 3y + 12
4y - 3y = 12 - 4
y = 8.
Answer. The son is 8 years now. The father's age is 4*8 = 32 years.
Solved.
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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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