Question 1070761
.
barbara's age is 5 years less than her brother's age if her age is increased by 3 times her brother's age the result is 51 years 
find each of their age.
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The "josgarithmetic" solution is WRONG.


<pre>
Let "x" be the Barbara's age, "y" be her brother age.
Then 

x = y-5,       (1)
x + 3y = 51.   (2)

Substitute expression (1) into equation (2), replacing y. You will get

(y-5) + 3y = 51.

4y - 5 = 51  --->  4y = 51 + 5 = 56   --->  y = {{{56/4}}} = 14.


Thus the brother's age is 14 years. Then the Barbara's age is 14-5 = 9 years.

<U>Answer</U>.  Barbara is 9 years. Her brother is 14 years.
</pre>

There is a bunch of lessons on age word problems 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Age-problems-and-their-solutions.lesson>Age problems and their solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Fresh-formulation-of-a-traditional-age-problem.lesson>A fresh formulation of a traditional age problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson>Really intricate age word problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Selected-age-word-problems-from-the-archive.lesson>Selected age word problems from the archive</A>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Age word problems</U>".



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One notice at the end. The phrase

"Barbara's age is 5 years less than her brother's age."

doesn't sound harmonically/naturally in English. They say

"Barbara is 5 years younger than her brother."


Same for "find each of their age."