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© 2014 Pacific Crest
185
Step
Explanation
10. Validate the
solution
Validate the solution.
Check the model:
In year 2000,
y
= 0 and
n
= 110 + 20 × 0 = 110
In year 2008,
y
= 8 and
n
= 110 + 20 × 8 = 110 + 160 = 270
Check the number of mobile phones in 2020:
?
?
110 20
510 = 110 20 20
510 = 110 400
510 510
n
y
= + ×
+ ×
+
=
YOUR
TURN!
Scenario:
A Health Maintenance Organization (HMO) suggests that a woman’s
recommended weight can be computed. For each inch over 5 feet tall, 5
pounds should be added to 100 pounds. Some women are, of course, 4 feet
11 inches or shorter, but this recommended weight is fairly reliable for 90%
of United States women. What does this HMO’s formula recommend for the
weight of a woman 6 feet 1 inches tall?
O
ops
! A
voiding
C
ommon
E
rrors
●
Misunderstanding ambiguous words
Example
: Interpret the sentence:
“There are six times as many girls as boys.”
6 times the number of girls is the number of boys
Let
g
= the number of girls, Let
b
= the number of boys: 6
• g
=
g
Why?
Careful reading is critical to solving word problems. If you don’t understand the
meaning in English, with precision, clarity, and accuracy, how can you possibly
represent the same idea mathematically? In this case, reading the sentence carefully
helps us understand that there are more girls than boys. We thus set up an equation
that demonstrates that fact:
g
= 6
• g
●
Incorrectly identifying variables
Example
: The driving time from Boston to New York is 8 hours shorter than the driving time
from Chicago to New York.
Let
d
= the difference Let
t
= the driving time:
d
= 8
t
Why?
If variables are not assigned correctly, you will end up calculating quantities that
have nothing to do with the problem you’re trying to solve. In this case, reading
carefully shows that the difference is a difference between two times. The shorter
time is between Boston and New York, because Boston is closer to New York than
Chicago is.
4.3 Interpreting a Word Problem