Question 1048479
.
Jack is 5 years older than his sister. The sum of their ages is 21. How old are Jack and his sister?
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<B>Solution 1</U> (using two equations in two unknowns)

<pre>
The condition says that

J - S =  5,   (1)   ("Jack is 5 years older than his sister")
J + S = 21.   (2)   ("The sum of their ages is 21")

Add the equations (1) and (2)  (both sides). You will get

2J = 5 + 21  --->  2J = 26  --->  J = {{{26/2}}} = 13.

Thus you found Jack's age. He is 13 years old.

Then his sister is 13 - 5 = 8 years old.

<U>Answer</U>.  Jack is is 13 years old.  His sister is 8 years old.

<U>Check</U>.  Please check yourself.
</pre>


<U>Solution 2</U>  (using one equation)

<pre>
Let J be Jack's age.
The Jack's sister age is (J-5) years.

The sum of their ages is 21, so

J + (J-5) = 21.

Simplify and solve for J.

2J - 5 = 21  --->  2J = 21 + 5 = 26  --->  J = {{{26/2}}} = 13.

We obtain the same result:  Jack is 13 years old; his sister is 8 years old.
</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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/04-OVERVIEW-of-lessons-on-age-problems.lesson>OVERVIEW of lessons on age problems</A>

in this site.


Read them and become an expert in solving age problems.


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It contains a lot of other word problems and many other interesting and useful things.