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Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?
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Let y be Evan's age, and
let x be the sister's age.
From the condition, you have these two equations
y - 3 = , (1) ("Three years ago, Evan was one third of his sister's age.")
2*(y+1) = x + 1. (2) ("In a year's time, Evan's age doubled will match his sister's age.")
From eq(1), 3*(y-3) = x - 3 ====> 3y - 9 = x - 3 ====> x = 3y - 6.
Now substitute it into eq(2). You will get
2*(y+1) = (3y-6) + 1 ====> 2y + 2 = 3y - 5 ====> y = 2 + 5 = 7.
Answer. Evan is 7 years old. His sister is 15 years old (from eq(2)).
Solved.
The solution by @josgarithmetic ("y = 10 Evan now") is W R O N G .
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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.