Lesson TRANSLATE age word problems into Algebreze

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.

Starting out with VARIABLES

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.

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

Putting everything together

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.

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 :

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

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER This is an equation! Solutions: F=26. Graphical form: Equation was fully solved. Text form: F+10=3*(F-24+10) simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( F+10=3*(F-24+10) ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Moved these terms to the left It becomes . Look at . Moved to the right of expression It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Solved linear equation equivalent to -2*F+52 =0 It becomes . Result: This is an equation! Solutions: F=26. Universal Simplifier and Solver Done!