21B Writing Equations for Word Problems

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2-1B Writing Equations for Word Problems
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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A Problem Solving Plan Using Models
Step 1 READ 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.
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Todd is five years older than Ben. The sum of
their ages is 35. Find both of their ages.
Step 1 READ 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.
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Todd is five years older than Ben. The sum of
their ages is 35. Find both of their ages.
Step 2 LABEL 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 least
information 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.
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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 Total ages
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.
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Read Todd is five years older than Ben. The sum
of their ages is 35. Find both of their ages.
Assign Labels let b Ben's age let b 5
Todd's age
Verbal Model Ben's age Todd's age Total
ages
Algebraic Model
DO NOT SOLVE YOUR EQUATION. THIS IS ALL YOU ARE
REQUIRED TO DO AT THIS TIME.
Note If a let quantity is more than one term
it belongs in parentheses.
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Example 1 In a game, Bens score was 3 times
Sams score. Together they scored 80 points.
Find their scores.
80
s
1. Assign Labels.
let s Sams score
let 3s Bens score
3s
Sams score Bens score total


2. Verbal Model.
3. Algebraic Model.
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Example 2 Megs age is 5 times Joses age. The
sum of their ages is 18. How old is each?
18
Let j Joses age
Let 5j Megs age
5j
Assign Labels.
j
Joses age Megs age Total

Verbal Model.

Algebraic Model.
Remember DO NOT SOLVE YOUR EQUATION.
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Example 3 A 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?
let s short piece
s
Assign labels.
let s 4 long piece
(s 4)
short piece long piece total


Verbal Model.
Algebraic Model.
Remember DO NOT SOLVE YOUR EQUATION.
Note If a let quantity is more than one term
it belongs in parentheses.
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Example 4 Together Gini and JoAnn own 87 pairs of
shoes. JoAnn has 25 more pairs than Gini has.
How many pairs does Gini have?
87
Let g Ginis shoes
Let g 25 JoAnns shoes

(g 25)
g
Assign Labels.
Ginis shoes JoAnns shoes Total
Verbal Model.

Algebraic Model.
Note If a let quantity is more than one term
it belongs in parentheses.
Remember DO NOT SOLVE YOUR EQUATION.
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HOMEWORK

• 2-A3 Handout A3