A Problem Solving Plan Using Models

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A Problem Solving Plan Using
Models
1.5
What you should learn
GOAL
GOAL
1
2
Translate verbal phrases into algebraic
expressions.
Use a verbal model to write an algebraic
equation or inequality to solve a real-life
problem, such as making a decision about
an airplane’s speed.
Why you should learn it
To solve real-life problems such as finding out how
many plates of dim sum were ordered for lunch.
A Problem Solving Plan Using
Models
1.5
GOAL
1
TRANSLATING VERBAL PHRASES
Learn the vocabulary in the table on page 32!!!
NOTE: Order will be important, even in addition and
multiplication. The question to ask is, “What number do I
start with?”
Example:
“A number increased by 3” is written as n + 3.
“3 increased by a number” is written as 3 + n.
EXAMPLE 1
Extra Example 1
Translate the phrase into an algebraic expression.
a. Six less than 4 times a number y.
4y – 6
b. Three more than the difference of five and a number n.
5–n+3
c. A number y decreased by the sum of 8 and the square of
another number x.
y – (8 + x2)
Checkpoint
Translate the phrase into an algebraic expression.
a. Eight more than the sum of two times a number y and
three.
(2y + 3) + 8
b. Four less than the sum of five and twice a number n.
(5 + 2n) - 4
1.5
GOAL
A Problem Solving Plan Using
Models
2
USING A VERBAL MODEL
When translating a verbal phrase or sentence look for the
word “is.” If it is there, you are nearly always looking at an
equation or inequality.
“is”: equation
“is less than” or “is greater than”: inequality
Remember to look for this 2-letter word!
Writing an Algebraic Model
We will write mathematical models to represent real-life
situations. These models may be expressions, equations, or
inequalities. We will use the steps shown in the text to solve
these situations.
VERBAL
MODEL
LABELS
ALGEBRAIC
MODEL
EXAMPLE 2
SOLVE
CHECK
Extra Example 2
You and your friends go to a music store to buy CD’s on
sale for $6 each. Together you spent $77.76, which
included a tax of $5.76. How many CD’s were bought?
Use the problem solving plan shown in the text.
VERBAL
MODEL
LABELS
ALGEBRAIC
MODEL
SOLVE
CHECK
Cost
per CD •
$6
Number
of CDs
n
=
Bill
$77.76
6n = 77.76 – 5.76
6n = 72
n = 12
Is 12 a reasonable answer? Yes.
ANSWER: You bought 12 CDs.
– Tax
$5.76
Checkpoint
Eight friends went to a restaurant for dinner. The waiter gave
them a bill for $130. At the register a tax and tip of $30 was
added to the bill. Use a verbal model and mental math to
find about how much each person should contribute to pay
an equal share of the bill.
# of
friends
8
•
Amount
each
pays
a
=
Bill
$130
8a = $130 + $30
$20
+
Tax
and
tip
$30
Extra Example 3
EXAMPLE 3
An investor finds a mutual fund that has an annual return of
10%. The investor wants to earn $250 in simple interest
by the end of one year. Use the formula I = Prt.
a. What should be the minimum amount invested?
b. If the investor wants to earn twice the amount of simple
interest, should the investment or the amount of time be
doubled? Explain.
Extra Example 3 (cont.)
VERBAL
MODEL
LABELS
ALGEBRAIC
MODEL
SOLVE
CHECK
Interest = Principal • Rate • Time
$250
p
0.10
yr
1 yr
0.10
$250  p 
 1 yr
yr
$250 = p • 0.10
Use mental math:
$250 is one-tenth
$2500 = p
of what number?
Is $2500 reasonable? YES.
ANSWER: The amount to invest is $2500.
Extra Example 3 (cont.)
To earn twice as much, the investor has two options. Either
twice as much money can be invested ($5000), or the $2500
can be invested for twice as long.
Checkpoint
1. A salesperson drives at a speed of 50 miles per hour. When
he is 175 miles from his destination, he remembers he has a
meeting in 3 hours.
a. At his current speed, will he be on time for his meeting?
No
b. At what minimum speed should he travel from this point
on if he wants to be on time for the meeting?
about 60 mi/h
QUESTIONS?
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