.
According to the first part of the condition, Anabelle is (y^2 - y) years older than Sarah.
According to the second part of the condition, Anabelle is (13y - y^2) years older than Sarah.
Actually, these two differences are the same:
y^2 - y = 13y - y^2.
Solve it:
2y^2 - 14y = 0
2y(y-7) = 0.
The only meaningful solution to the problem is y = 7.
Answer. Sarah is 7 years old now.
Anabelle is 49 yers old now.
The differences in ages are: 1) 49-7 = 42; b) 13*7 - y^2 = 91-49 = 42.
! Correct !
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.