SOLUTION: The sum of paul and beth’s ages is 67. Eight years ago paul was twice as old as beth. How old is each now?

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Question 1121868: The sum of paul and beth’s ages is 67. Eight
years ago paul was twice as old as beth. How old is each now?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28p%2Bb=67%2Cp-8=2%28b-8%29%29


highlight%28b=25%29-----Beth
-
highlight%28p=42%29-----Paul



---
student requested solution steps.

p, Paul's age now
b, Beth's age now

The description translated literally is this system:
system%28p%2Bb=67%2Cp-8=2%28b-8%29%29

Second Equation Simplification,
p-8=2b-16
p=2b-8

Substitute this into the age-sum equation:
p%2Bb=67
%282b-8%29%2Bb=67
3b-8=67
3b=75
b=25-------Beth's age is found.

Answer by ikleyn(52783) About Me  (Show Source):
You can put this solution on YOUR website!
.
Since the sum of their ages is 67, 8 years ago this sum was 67 - 2*8 = 51.


So, 8 years ago the sum of their ages was 51 year and Paul was twice the Beth's age.


Then it is clear that 8 years ago Beth was 17 years old and Paul was 34 years old.


So now their ages are  17+8 = 25  (Beth)  and  34+8 = 42 (Paul).

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.