Transcript Sullivan College Algebra: Section 1.2

Sullivan Algebra and
Trigonometry: Section 1.2
Objectives of this Section
• Translate Verbal Descriptions into Mathematical
Expressions
• Set Up Applied Problems
• Solve Interest Problems
• Solve Mixture and Motion Problems
• Solve Constant Rate Job Problems
Translating English into Math: Examples
English
Math Translation
is, are, was
=
of
Multiplication
5 more than a number
5+x
8 less than a number
x-8
The quotient of a number and 6
x/6
3 times a number
3x
Steps for Setting Up Applied Problems
Step 1: Read the problem carefully, perhaps two or
three times. Identify what you are looking for.
Step 2: Assign a letter (variable) to represent what
you are looking for. Express any remaining
unknown quantities in terms of that variable.
Step 3: Make a list of known facts and translate
them into mathematical expressions. These may
take the form of an equation or later, an inequality.
Step 4: Solve the equation for the variable and
answer the question using a sentence.
Step 5: Check your answer with the facts of the
problem.
Example: Yolanda, Mary, and Sophie won $200,000
playing the lottery. Based on how much each
contributed to buy the ticket, Mary gets four fifths of
what Yolanda gets, while Sophie gets three fourth of
what Mary gets. How much does each receive?
y: amount received by Yolanda
m: amount received by Mary
s: amount received by Sophie
y  m  s  200000
y  m  s  200000
4
m y
5
3
s m
4
3 4 
  y
45 
3
 y
5
4
3
y  y  y  200000
5
5
12
y  200000
5
y  $83,333.33
4
m  ($83,333.33)  $66,666.67
5
3
s  ($83,333.33)  $50,000
5
Example: The suggested list price of a new car is
$16,000. The dealer cost is 80% of list. How much
will you pay if the dealer is willing to accept $2000
over the cost for the car?
x: cost to you
y: cost to the dealer
()80%0.81600012800
===
yoflist
=+=+=
xy
2000200012,80014,800
Example: The purity of gold is measured in karats,
with pure gold being 24 karats. Other purities of
gold are expressed as proportional parts of pure
gold. Thus, 18 karat gold is 18/24, or 75% pure
gold. How much 12 karat gold should be mixed
with 18 karat gold to obtain 50 grams of 14 karat
gold?
x: amount of 18 karat gold
y: number of grams of 12 karat gold
x  y  50
18 12
14
x  y  (50)
24 24
24
18 x  12(50  x )  14(50)
+-=
xx
1860012700
6x  100
50
x
3
100
y
3
Example: Jeff can mow his lawn in 3 hours.
Melissa can mow the same lawn in 2 hours.
Working together, how long will the job take,
assuming that there is no gain or loss of efficiency
working together.
t: hours needed to complete the job together
Hours to do job
Fraction of Job Done in 1 Hour
Jeff
3
1/3
Melissa
2
1/2
Together
t
1/t
Part done by Part done by
Part done together
+
=
Jeff in 1 hour Melissa in 1 hour in 1 hour
t+=
32
111
6t=
51
t=
56
11==hour and 12 minutes
61
t=
55