WordProblemReviewFall08

WordProblemReviewFall08 - 
 Word
Problem
Review


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Unformatted text preview: 
 Word
Problem
Review
 The
problems
you
will
review
here
do
not
require
any
calculus.
They
are
practice
in
setting
up
problems
ready
for
the
 use
of
calculus
techniques.

They
are
important
preparation
for
problems
coming
later
in
the
course.


If
you
can’t
find
 the
needed
equations
from
the
problem
statement
you
will
not
be
able
to
solve
the
problem.
 Text
References:
 Linear
Equations
 
 
 
 
 
 
 
 
 
 Other
equations
 Section

 


1.3
 
 
 
 


1.4
 
 
 
 
 
 
 Examples
 6,
8
 
 
 
 
 
 
 
 
 
 
 



 Exercises
 
 
 
 
 
 Try
It
6:

Ex
79
–
83,
85,
86,
88,
89


 
 
 
 Some
of
these
problems
can
be
answered
using

numerical

 methods
instead
of
finding
equations.

This
won’t
help
much
in
 
 Calculus.
 69,
71
–
73,
75
 
 
 Extra
Practice
Problems
 Write
equations
that
express
the
following:

 1. 2. 3. 4. 5. The
area
of
a
circle,
A,
in
terms
of
its
radius,
r.
 The
circumference
of
a
circle,
C,
in
terms
of
its
radius,
r.
 The
area
of
a
circle,
A,
in
terms
of
its
circumference,
C.
 The
volume,
V,
of
a
sphere
in
terms
of
its
radius,
r.
 The
volume,
V,
of
a
cube
in
terms
of
its
side
length,
x.
 
 6. A
rectangle
has
perimeter
36m.

Let
the
length
of
one
side
be
x.

Find
an
equation
for
the
area,
A,

of
the
 rectangle
in
terms
of
x.
 
 7. Three
adjoining
,
identical,
rectangular
pens
are
constructed
using
108m
of
fencing.
Let
the
length
of
one
side
of
 a
pen
be
x
and
the
other
be
y.

Find
an
equation
for
the
total
area,
A,

of
all
three
pens
in
terms
of
x.
Then
find
A
 in
terms
of
y.
 
 8. A
pen
is
constructed
with
one
side
along
a
river
and
therefore
not
requiring
a
fence.

The
total
area
enclosed
is
 96m2
.

Let
x
be
the
length
of
the
side
parallel
to
the
river
and
y
be
the
other
side
length.

Find
an
equation
for
 the
needed
fence
length,
F,

(i)

in

terms
of
x,
and
(ii)
in
terms
of
y.
 
 9. A
rectangular
pen
is
to
be
constructed
using
fencing
along
three
sides
that
costs
$10/m
and
the
fourth
side
costs
 $15/m.
48m2
is
to
be
enclosed.

(i)

Find
an
equation
for
the
total
cost,
C,
in
terms
of
x,
the
length
of
the
side
that
 costs
$15/m.
(ii)
Find
an
equation
for
the
total
cost,
C,
in
terms
of
y,
the
length
of
the
side
that
costs
$10/m.

 
 10. A
rectangular
pen
is
to
be
constructed
using
fencing
along
three
sides
that
costs
$10/m
and
the
fourth
side
costs
 $15/m.
$7500
is
available
for
the
work.

(i)

Find
an
equation
for
the
total
area
enclosed,
A,
in
terms
of
x,
the
 length
of
the
side
that
costs
$15/m.
(ii)
Find
an
equation
for
the
total
area
enclosed,
A,
in
terms
of
y,
the
length
 of
the
side
that
costs
$10/m.

 
 
 
 11. A
rectangular
poster
is
to
contain
180cm2
of
print.

The
margins
at
the
top
and
bottom
of
the
poster
are
to
be
 2.5cm
wide.

The
margins
on
each
side
of
the
poster
are
to
be
2cm
wide.

Find
an
equation
that
gives
the
 amount
of
paper
used
(total
poster
area)
in
terms
of
one
of
the
dimensions.

 
 12. A
small
business
uses
a
minivan
to
make
deliveries
on
a
route
that
is
90
km
long.

The
cost
per
hour
of
gasoline
is
 
where
 
is
the
average
speed
of
the
minivan
in
km/h.

The
driver
is
paid
$20
per
hour.
Find
an
 equation
for
the
total
cost
in
terms
of
the
average
speed,
 .
 
 13. A
home
gardener
estimates
that
if
she
plants
16
apple
trees
the
average
yield
will
be
80
apples
per
tree.

 However,
because
of
overcrowding
for
each
additional
tree
planted
the
yield
will
decrease
by
4
apples
per
tree.
 Assume
this
is
a
linear
relationship.

Find
an
equation
for
the
total
yield
in
terms
of
the
number
of
trees
planted.
 
 In
Cost
,
Revenue
and
Profit
problems,
p
is
conventionally
used
for
the
selling
price
of
an
item
and
x
represents
the
 number
of
items
made
and
sold.

p
is
given
by
the
demand
equation.


In
some
problems
this
is
a
linear
equation
 you
are
asked
to
find,
from
information
supplied.
 Cost
is
given
by
C(x),
Revenue
by
R(x)
and
Profit
by
P(x)
.
 
 P(x)
=
R(x)
–
C(x)
 
 14. If
the
demand
equation
is
 
and
the
cost
function
is
 ,
find
an
equation
for
the
 profit
function.
 
 15. When
a
tourist
trap
charges
$5
for
admission,
attendance
is
an
average
of
180
people.

For
every
increase
of
 $0.10
there
is
an
average
loss
of
1
customer.

Assume
that
the
relationship
between
admission
price
and
 attendance
is
linear
and
find
the
demand
function
followed
by
the
revenue
function
for
this
tourist
trap.
 
 16. A
theatre
estimates
that
when
it
charges
$26
for
a
ticket,
its
concert
attendance
is
1000,
and
for
every
$2
drop
 in
ticket
price
its
audience
increases
by
100.

Concession
sales
work
out
to
an
average
of
$4
per
concert‐goer.

 Find
the
Revenue
function.
 
 17. An
appliance
store
determines
that
in
order
to
sell
x
stoves,
each
stove
must
be
priced
according
to
the
demand
 equation
p
=
280
–
0.4x.

It
also
determines
that
the
total
cost
of
producing
x
stoves
is
C(x)
=
5000
+
0.6x2.

Find
 the
revenue
function
and
the
profit
function.
 
 18. All
300
rooms
in
a
resort
are
booked
when
the
resort
charges
$80
per
day
for
a
room.

For
every
$1
increase
in
 room
charge
1
less
room
is
occupied.
Assume
a
linear
relationship.

(i)

Find
the
demand
equation,
that
is,
find
 an
equation
for
the
room
charge,
p,
in
terms
of
x,
the
number
of
rooms
occupied.

(ii)

Find
the
revenue
function
 for
the
hotel.

(iii)

If
each
occupied
room
costs
$22
per
day
to
maintain,
find
the
profit
function
for
the
resort.
 
 
 
 
 
 
 ...
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