Translating Verbal Descriptions
into Mathematical Expressions
• Let’s look some examples that help you
translate verbal descriptions into
mathematical expressions:
• Example 1:
For uniform motion, the velocity of an
object equals the distance traveled divided
by the time required.
Solution: if v is the velocity, s the distance
and t the time, then v=s / t
Example 2:
• Let x denote a number:
The number 5 times as large than x is:
5x
The number 3 less than x is:
x-3
The number that exceeds x by 4 is:
x+4
The number that, when added to x, give 5 is:
5-x
PROBLEM SOLVING
Interest problems
Formula : I=P.r.t
• Example :
• Kelly borrows $500 for 6 months at the
simple interest rate of 9% annually. What
is the interest that Kelly will be charged in
this loan?. How much does she owe after
this time?
Solution:
• That the money The rate f interest is
annually, so the time that the money is
borrowed must be expressed in years.
• The interest charged would be the
principal $500, times the rate of
interest(9% = 0.09) times the time in years
½
• Interest Charged= I =Prt= (500)(0.09)(1/2)
• I= $22.50
After 6 months, Kelly will owe what
she borrowed plus the interest:
• $500 + $22.50 = $522.50
Mixture Problem
Problems that combine to or more
quantities to form a mixture.
• Example : The manager of Starbucks store
decides to experiment with a new blend of
coffee. He will mix some B grade Colombian
coffee that sells for $5 per pound with some A
grade Italian coffee that sells for $10 per pound
to get 100 pounds of the new blend; the selling
price for the new blend is $7 per pound. How
many pounds of each coffee he needs?
Solution:
• Let x represent the numbers of pounds of
the B grade Colombian coffee, then 100-x
represents the Italian coffee
• Now translate this to a mathematical
expression
• 5X + 10(100-X) = 7(100)
Solving the equation:
•
•
•
•
5X + 1000 – 10X = 700
-5X = -300
X=60
The manager should blend 60 pounds of
Colombian Coffee with 100-60= 40
pounds of Italian Coffee
Uniform Motion Problems:
If an object moves an average
velocity v, the distance s covered in
time t is given by v=s/t
• Example: Shadekah who is a long-distance
runner, runs at an average velocity of 8 miles
per hour (mi/hr). Two hours after she leaves
your house, you leaves in your Honda and
follow the same route. If your average velocity
is 40 mi/hr, how long time will it be before you
catch up to Shadekah. How far will each of you
be from your home
Solution:
• Let t be the time that it takes the Honda to
catch up to Shadekah. When this occurs the
total time elapsed for Shadekah is t+2 hours.
• Set up the following table:
v= s / t
»
s= v. t
Velocity
(mph)
Time
(hr)
Distance
(mi)
Shadekah
8
t+2
8(t+2)
Honda
40
t
40t
Solution:
• Since the distance traveled is the same, we are
led to the following equation:
8(t+2)=40t
8t+16=40t
32t=16
t= ½ hr
• It will take the Honda ½ hr to catch up to
Shadekah. Each will have gone 20 miles
CONSTANT RATE JOB
PROBLEMS
• This involves jobs that are performed at a constant
rate. The assumption is that, if a job can be done in t
units of time, 1/t of the job is done in 1 unit of time.
• Example:
• At 10:00 a.m. Danny is asked by his father to weed the
garden. From past experience, Danny knows this will
take him 4 hours, working alone. His older brother. Mike
when it is his turn to do this job, requires 6 hours. Since
Mike wants to go golfing with Danny and has a
reservation for 1p.m., he agrees to help Danny. When
will they finish if they work together? Can they make the
golf date?
Solution
Hours to do Job Part of Job done
in 1 hour
Danny
4
1/4
Mike
6
1/6
Together
t
1/t
Translating to a mathematical
expression
• 1/4 +1/6 = 1/ t
3+2 = 1
12
t
5 = 1
12
t
5t = 12
so t =12/5
Working together, the job can be done in 12/5
hours or 2 hours 24 min. They should make the
golf date, since they will finish at 12:24 p.m.