.
Solution 1 : two unknowns, two equations
S - K = 3 (1)
(S-5) + (K-5) = 41 (2)
Equivalently
S - K = 3 (1')
S + K = 51 (2')
Add equations (1') and (2'). You will get
2S = 3 + 51 = 54 ====> S = 54/2 = 27.
Answer. Susan is 27; Karen is 24 years old.
Solution 2 : one unknown, one equation
(K-5) + ((K+3)-5) = 41 (5 years ago . . . )
2K - 7 = 41
2K = 41 + 7 = 48
K = 24,
and you get the same answer.
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It is a very standard age word problem.
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.