Lesson TRANSLATE age word problems into Algebreze

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Age word problems are a little silly in the sense that you are not going to encounter many problems like that in real life. What they are useful for is teaching students how to translate English phrases into the Algebraic language that longjonsilver is calling algebreze.

Algebra deals with variables like x or y, expresisons like x-2y, and equations such as x=2y+3.

Age word problems are exercises in writing such equations based on the problem. In this lesson, I will mention how to start solving age problems and several typical phrases and how to translate them into Algebreze.

<H4>Starting out with VARIABLES</H4>

Almost all word problems require you to introduce variables. Usually, a great choice of variables is first letters of names of the persons involved. For example, if the problem talks about ages of Alice and Bob, you can use variable A for Alice's age and B for Bob's age.

Now, some common phrases using names of Alice and Bob:

<UL>
 <LI>Bob is 3 years older than Alice -- B=A+3</LI>
 <LI>Bob is 3 years younger than Alice -- B=A-3</LI>
 <LI>In five years, Bob will be... -- B+5</LI>
 <LI>Five years from now, Bob will be... -- B+5</LI>
 <LI>Five years ago, Bob ... -- B-5</LI>
 <LI>Alice is 4 times older than Bob -- A=4B</LI>
 <LI>The difference of Alice and Bob's age is -- A-B</LI>
 <LI>How old will Bob be in 7 years? -- Find out B and then B+7</LI>
</UL>

<H3>Putting everything together</H3>

<BLOCKQUOTE>Craig is 24 years younger than his father. In 10 yrs,
Craig's father will be three times as old as Craig will be. Find their
ages now. </BLOCKQUOTE>

Step 1: Pick variables, say C (for Craig) and F (for Father).

Craig is 24 years younger than his father. Translation into Algebreze: C=F-24.

In 10 years, Craig's father... Translation: F+10

... F+10 will be three times as old as Craig will be. Translation: F+10=3(C+10).

So, our word problem boils down to :

{{{system( C=F-24, F+10=3(C+10) ) }}}

Then solving it is just straight math. Substitute C in the second equation with F-24: F+10 = 3(F-24+10).

*[invoke explain_simplification "F+10=3(F-24+10)"]

So, F is age of father and it is 26. Then C=F-24, or C=2.

Answer: Craig is 2 years old and his father is 26 years old.