.
M - 5 = 3*(S-5) (1) (five years ago . . . )
(M + 6 ) + (S + 6) = 82. (2) (in 6 years time . . . )
Simplify and solve the system.
M - 5 = 3*S - 15
M + S + 12 = 82
M = 3*S - 10, (1')
M + S = 70. (2')
From (1'), substitute M = 3*S - 10 into eq(2') to get
(3*S - 10) + S = 70
4S = 80 ====> S = 20 is the son's age.
Then the mother age is M = 3*S - 10 = 3*20-10 = 50 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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There is an easy way to solve this problem mentally (recreational mode).
In 6 yrs time the sum of their ages will be 82 ====>
the sum of their ages NOW is 82 - 2*6 = 70 ====>
the sum of their ages 5 years ago was 70 - 2*5 = 60 ====>
the sum of their ages 5 years ago was 60 and the mother's age was 3 times the son's age ====>
5 years ago the son was 15 years old, while the mother was 45 years old ====>
Now they are 20 and 50 years old.