Solving word problems is a lengthy multistep process, which can be summarized as follows: PESN = Picture-Equation-Step-Nudify. We The steps are
- Picture = draw the picture corresponding to the problem
- Equation = write down the equation from the picture
- Step = draw the Step that outlines the substitution process
- Nudify = use the nudify-swap cycle for the substitution method
Let's apply this sequence to problem #4 below.
The picture "P" for this problem is a dual timeline. Above the timeline, we write ages "then" and below the timeline, we write ages "now". Shape variables will be "then" and letter variables will be "now". In pictures, we have
+------+ +--+ Definition | H-25 | and /J-25\ +------+ +------+ so, the picture is +---------+ +--+ then | 5 + J/3 | (1) /J-25\ +---------+ +------+ | | timeline --> +----------------------+ | | now H J = 2H - 26 (2)
Step "E" for equation is read off the picture, which is simply (1) & (2). Finally, step "SN" Step-Nudify has been depicted in the the "Linear System" section.
1. Samantha is 8 and two-third years older than Jason. The sum of their ages is 23 years. How old is Jason?
2. Brian is three years older than Sydney. The sum of the ages of Brian and Sydney is seven. How old is Brian?
3. Ryan was born 6 and one-fourth years after Alexander. The sum of their ages is 66 and eleven-twelfth years. How old is Alexander?
4. Twenty-five years ago, Hailey was five more than one-third as old as Jason was. Today, Jason is twenty-six less than two times the age of Hailey. How old is Jason?
5. Hunter is five times as old as Rachel. Thomas is twice as old as Rachel. Rachel is twelve years younger than Thomas. How old is Hunter?
6. Kayla would be one-half as old as Nathan if Kayla were four years older. Nathan is eight less than three times as old as Kayla. How old is Nathan?
7. Isaac is nine years older than Kylie. Isaac is four times as old as Brian was three years ago. Brian is eighteen years younger than Isaac. How old is Kylie?
8. Samantha has a total of twenty seven pennies, nickels and quarters. She has a total of $2.11. Together her number of coins in nickles & pennies are twice the count in quarters & pennies. How many of each coin does she have?
9. Jordan has a total of one hundred thirty nickels, dimes and quarters. He has three and a half times as many nickels as dimes, and one-half as many quarters as dimes. How much money does he have?
10. Austin has nickels, dimes and quarters. He has a total of $17.65. He has eleven fewer quarters than nickels and six times as many dimes as quarters. How many of each coin does he have?
11. Cody has pennies, dimes and quarters. He has a total of $17.64. He has two times as many quarters as dimes and one-third as many dimes as pennies. How many of each coin does he have?