@qAGE TUTORIAL -- PART 1. This is a Tutorial on Age Word Problems. If you find a question confusing, use the `HELP' key.@pIf the Tutorial seems too easy, use the `Skip Problem' key. (Any key to continue.)@hThere are always two HELP's available. The second time you press the HELP key you get the correct answer.@hThe `Skip Problem' key will take you to the next problem, or to the next part of the Tutorial.@i(0)@jWord problems are difficult because there is so much information. Homework Helper Math provides grids to help organize this information.&d(0,)@jAge problems compare the ages of two people at two different times. This type of problem shows how to use a grid.@dg10&c(1,George)&c(2,Mother)&d(0,This grid would be used to compare George's age with his mother's age.) @jHere are some simple problems to show how data is entered into the grid.&d(0,)&d(2,)@jIf George is 25 years old now, how old will he be in 5 years?&d(3,Age Now)@pBegin by entering George's Age Now.@hRead the problem carefully.&qGeorge is 25 years old now&q@hEnter `25' and press the <Return> key.@i(4,i,25)&d(6,Difference)@pThe problem is to find George's age in 5 years. He will be 5 years older then, indicate this by entering `+ 5'.@hYears into the future are shown by adding to George's Age Now.@hEnter `+5' and press the <Return> key.@i(7,i,+5)&d(9,Age Then)&d(0,The Equation Idea to figure Age Then is:\n   Age Now  +  Difference  =  Age Then.)&c(13,Age Now + Difference  =  Age Then)&d(0,For ages in the future, years are added to Age Now. For ages in the past, years are subtracted.)@pNow write an expression that represents George's age in five years (Age Then).@hFor George:\n\f05Age Now + Difference = Age Then\n\f05   25   +   (+5)@hEnter `25 + 5' and press the <Return> key.@i(10,i,25+5)@s &d(7,)&d(10,)@jIf George is 25 years old now, how old was he 8 years ago?&d(0,)@pThe problem is to find George's age 8 years ago. He was 8 years younger then. Indicate this by entering `-8'.@hYears into the past are shown by subtracting from George's Age Now.@hEnter `-8' and press the <Return> key.@i(7,i,-8)@pNow write an expression that represents George's age 8 years ago (Age Then).@hFor George:\n\f05Age Now + Difference = Age Then\n\f05   25   +   (-8)@hEnter `25 + (-8)' and press the <Return> key.@i(10,i,25+(-8))@s &d(4,)&d(7,)&d(10,)@jIf George is `x' years old now, how old will he be in 20 years?&d(0,)@pBegin by entering George's Age Now.@hGeorge's Age Now is represented using the variable `x'.@hEnter the letter `x' and press the <Return> key.@i(4,i,x)@pThe problem is to find George's age 20 years from now. He will be 20 years older then.@hYears into the future are shown by adding to George's Age Now.@hEnter `+20' and press the <Return> key.@i(7,i,+20)@pNow, use the Equation Idea to write an expression that represents George's age in 20 years (Age Then).&w(13)@hFor George:\n\f05Age Now + Difference = Age Then\n\f05   x    +   (+20)@hEnter `x + 20' and press the <Return> key.@i(10,i,x+20)@s @qGeorge's mother is 20 years older than George. Represent their ages now, and in 6 years.@dg10&c(1,George)&c(2,Mother)&d(3,Age Now)&d(6,Difference)&d(9,Age Then)&d(0,)@pUse a variable to represent George's Age Now. This is the smaller quantity.@hUse a letter, such as `g' to represent George's Age Now.@hEnter `g' and press the <Return> key.@i(4,i,&v)@pRepresent George's mother's Age Now in terms of George's Age Now.@hGeorge's Age Now is `&v', and his mother is 20 years older.@hEnter `&v+20' and press the <Return> key.@i(5,i,&v+20)@pThe problem is to represent their age in 6 years. They will be 6 years older then.@hYears into the future are shown by adding to George's Age Now.@hEnter `+6' and press the <Return> key.@i(7,i,+6)&d(8,+6)&c(13,Age Now + Difference  =  Age Then)&d(0,The Equation Idea to figure Age Then is:\nAge Now + Difference = Age Then)@pUse the Equation Idea to write an expression that represents George's age in 6 years (Age Then).&w(13)@hFor George:\n\f05Age Now + Difference = Age Then\n\f05   &v    +   (+6)&w(13)@hEnter `&v + 6' and press the <Return> key.@i(10,i,&v+6)@pNow write an expression that represents George's mother's age in 6 years (Age Then).@hFor George:\n\f05Age Now + Difference = Age Then\n\f05  &v+20  +   (+6)@hEnter `&v + 20 + 6' and press the <Return> key.@i(12,i,&v+26)@jGeorge's mother is 20 years older than George. In 6 years George's mother will be twice as old as he is. How old are they now?&d(0,)@pUse the Multiplier Window to show the relation between George's Age Then and his Mother's Age Then.@hIn 6 years George's Mother will be 2 times George's age.@hEnter `2' and press the <Return> key.@i(11,i,2)&c(13,(&v+6)  * 2  =  &v+26)@pUse the Calculator to solve the equation for `&v' (George's Age Now).@hThe Calculator solves equations for you and displays steps in the solution.@hRemember to multiply both &v and 6 by 2. Enter `&v=14' and press the <Return> key.@i(13,i,&v=14)@pNow you are ready to enter your answers to the problem in the grid.&qHow old are they now?&q@h`&v' represents George's Age Now.@hSince &v=14, George is `14' years old now.@i(4,i,14)@pEnter George's mother's Age Now.@h"&v+20" represents George's mother's Age Now.@hSince &v=14, George's mother's Age Now is 14+20, or `34' years old.@i(5,i,34)@rCHECK@pReread the problem. Check your answers. Evaluate the remaining expressions in the grid.@hSubstitute for `&v' in the expression for George's Age Then. Then calculate the result.@hGeorge's Age Then is &v+6, so in 6 years he will be 14+6, or `20' years old.@i(10,i,20)@hSubstitute for `&v' in the expression for George's mother's Age Then. Then calculate the result.@hGeorge's mother's Age Then is &v+26, so in 6 years she will be 14+26, or `40' years old.@i(12,i,40)&d(0,Check your work. 2 times George's Age Then should equal George's mother's Age Then.)&d(0,This completes the first part of the Tutorial.)|