Writing Equations for Word Problems

1. Writing Equations for Word Problems

2. A Problem Solving Plan Using Models Step 1READ the problem very carefully. Step 2 LABEL the unknown by writing a “LET STATEMENT”. Step 3 Write a VERBAL MODEL that represents the logical set up of the problem. Step 4 Write the ALGEBRAIC MODEL. The Algebraic Model is the same as the equation that represents the Verbal Model.

3. Todd is five years older than Ben. The sum of their ages is 35. Find both of their ages. Step 1READ the problem very carefully. Decide what is asked for and what information is given. If you need to, make a sketch. You are asked to find their ages when only the sum is given.

4. Todd is five years older than Ben. The sum of their ages is 35. Find both of their ages. Step 2LABEL one unknown number by writing a “Let Statement”. Choose a variable appropriate to the problem. How do you know which person should represent the variable? A good rule of thumb is to let the variable represent whomever they give the leastinformation about in the problem. Another good tip is to let the variable represent the answer you are looking for. let b = Ben's age Then write all other unknown numbers in terms of the variable already used. let b + 5 = Todd's age In these problems you may NOT use more than one variable You may not have variable “t ” and a variable “b”.

5. Todd is five years older than Ben. The sum of their ages is 35. Find both of their ages. Step 3 Write a VERBAL MODEL that represents the logical set up of the problem. Ben's age + Todd's age = Totalages Whenever you see that you have a total your verbal model will almost always be one thing added to the other is equal to the total. Verbal models are written with WORDS not numbers or variables. Step 4 Write the ALGEBRAIC MODEL. The Algebraic Model is the same as the equation that represents the Verbal Model. Write the equation by substituting your “let statements" into your Verbal Model. This is "Translating" the Verbal Model into an equation.

6. ReadTodd is five years older than Ben. The sum of their ages is 35. Find both of their ages. Assign Labels letb=Ben's ageletb+ 5=Todd's age Verbal Model Ben's age + Todd's age = Total ages Algebraic Model Note: If a “let” statement is more than one term it belongs in parentheses.

7. Example 1In a game, Ben’s score was 3 times Sam’s score. Together they scored 80 points. Find their scores. 80 Assign Labels. s let s = Sam’s score let 3s = Ben’s score 3s Verbal Model. Sam’s score + Ben’s score = total + = Algebraic Model.

8. Example 2Meg’s age is 5 times Jose’s age. The sum of their ages is 18. How old is each? 18 Let j = Jose’s age Let 5j = Meg’s age 5j j Assign Labels. Jose’s age + Meg’s age = Total + Verbal Model. = Algebraic Model.

9. 24 Example 3A ribbon 24 feet long is cut into two pieces. The larger piece is four feet longer than the shorter piece. What are the lengths of the pieces? Assign labels. let s = short piece s let s + 4 = long piece (s + 4) Verbal Model. short piece + long piece = total + = Algebraic Model. Note: If a “let” quantity is more than one term it belongs in parentheses.

10. Example 4Together Gini and JoAnn own 87 pairs of shoes. JoAnn has 25 more pairs than Gini has. How many pairs does Gini have? 87 + (g+ 25) Let g = Gini’s shoes Let g+ 25 = JoAnn’s shoes g Assign Labels. Verbal Model. Gini’s shoes + JoAnn’s shoes = Total = Algebraic Model. Note: If a “let” statement is more than one term it belongs in parentheses.