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A mother told her son that the son was already 10 years old when she was at his age.
Then the mother said to the son, “I will be 88 years old when you are at my age.”
How old was the mother when her child was born?
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In order for you better understand the condition, I will re-write it in this EQUIVALENT form.
A mother told her son that the son was already 10 years old when she was at his
age.
Then the mother said to the son, “I will be 88 years old when you are at my age.”
How old was the mother when her child was born?
Now I am ready to solve it and to present the solution.
Let x be the mother age when her son was born.
It means that the mother is x years older than the son is. (*)
From the first statement of the problem, the son's current age is (10+x) years (now).
Hence, the mother's current age is (10+x+x) = (10 + 2x) years (now).
From the second statement of the problem, the son's age will be (10+2x) years, when the mother will be 88 years old.
At that time, the difference between their ages will be (88- (10+2x)) years,
and it will be exactly x years, as noticed in (*).
It gives you this equation
88 - (10+2x) = x.
Simplify and find x
88 - 10 - 2x = x
78 = 3x
x = 78/3 = 26.
ANSWER. The mother was 26 years old, when the son was born.
CHECK. Hence, the son's current age is 26+10 = 36 years now;
the mother's current age is 36+26 = 62 years now;
88-62 = 26 years. In 26 years the mother will be 88 years old, while the son will be 36+26 = 62 years,
which exactly is the mother's current age. ! Correct !
Solved.
Well-tricked problem (!)
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There is a bunch of lessons on age word problems
- Age problems and their solutions
- HOW TO algebreze and to solve age problems?
- A fresh formulation of a traditional age problem
- Really intricate age word problems
- Selected age word problems from the archive
- Age problems for mental solution
- Age problem for three participants
- Miscellaneous age problems
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.