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MTH001
Elementary Mathematics
LECTURE #
21
RATIO AND
PROPORTION
MERCHANDISING
OBJECTIVES
The
objectives of the lecture
are to learn about:
·
Module
3
·
Ratio
and Proportions
·
Merchandising
MODULE
3
Module
3 has the following
content:
·
Ratio
and Proportions
·
Merchandising
·
Mathematics
of Merchandising
(Lectures
13-16)
ESTIMATING
USING RATIOS-EXAMPLE 1
In
the previous lecture, we
studied how ratios can be
used to determine
unknowns.
Here is another example with
a slightly different approach.
Here, the
ratios
between the of quantities
are known.and data of only
one quantity is
known.
How do We will estimate the
total quantity that can be
made? It is the
quantity
of orange juice that will
determine the total quantity
that can be made.
Again
the method is to use the
ratio of the unknown to the
known.
Punch
recipe
In
a punch the ratio of mango
juice, apple juice and
orange juice is 3:2:1. If
you
have
1.5 liters of orange juice,
how much punch can you
make?
Calculation
Mango
juice : Apple juice : Orange
juice
3
:
2
:
1
Total
= 3+2+1 = 6
X
(say) : Y(say) :
Z(say)
?
:
?
:
1.5litres
Total
= ? litre
Mango
juice (X) = (3/1)×1.5 = 4.5
litre
Apple
juice (Y) = (2/1)×1.5 = 3.0
litre
Orange
juice (Z)
=
1.5 litre
Total
Punch = 4.5 + 3.0 +
1.5
=
9 litres
EXCEL
Calculation
The
method used is the same as
used in previous
examples.
Page
138
MTH001
Elementary Mathematics
ESTIMATING
USING RATIOS-EXAMPLE 2
In
a punch ratio of mango
juice, apple juice and
orange juice is 3 : 2 :
1.5.
Quantity
of If you have 500 litres of
orange juice find how much
mango and
apple
juices are required to make
the punch.
Punch
recipe
The
ratio of mango juice, apple
juice and orange juice is 3
: 2 : 1.5 If you
have
500
milliliters of orange juice, how
much mango juice and
apple juice is
needed?
Mango
juice : Apple juice : Orange
juice
3
:
2 :
1.5
Total
= 6.5
X
(say) :
Y(say)
:
Z
(say)
?
:
? :
500
litres
Total
= ? litres
Mango
juice (X) = (3/1.5)*500 =
1000 litre
Apple
juice (Y) = (2/1.5)*500 =
667 litre
Orange
juice (Z )
=
500 litre
Total
Punch = 1000 + 667 +
500
=
2167 litre
EXCEL
Calculation
Here
also ratios were
used.
Mango
juice = B45/B47*D47
Apple
juice = B46/B47*D47
Orange
juice = D47
Page
139
MTH001
Elementary Mathematics
EXAMPLE
In
a certain class, the ratio
of passing grades to failing
grades is 7 to 5. How
many
of the 36 students failed
the course?
The
ratio, "7 to 5" (or 7 : 5 or 7/5),
tells you that, of every 7 +
5 = 12 students, five
failed.
That
is, 5/12 of the class
failed.
Then
(5/12 )(36) = 15 students
failed.
PROPORTION
a/b
= c/d
...the
values in the "b" and
"c" positions are called
the "means" of the
proportion,
while
the values in the "a"
and "d" positions are
called the "extremes" of
the
proportion.
A basic defining property of a
proportion is that the
product of the
means
is equal to the product of
the extremes. In other
words, given:
a/b
= c/d
...it
is a fact that ad =
bc.
PROPORTION-EXAMPLES
Is
24/140 proportional to
30/176?
Check:
140×30
= 4200
24×176
= 4224
So
the answer is that given
ratios They are not
proportional.
PROPORTION
EXAMPLE 1
Find
the unknown value in the
proportion: 2 : x = 3 : 9.
2:x=3:9
First,
convert the colon-notation
ratios to fractions:
2/x
= 3/9
Then
solve: Cross
multiply
18
= 3x
6=x
Page
140
MTH001
Elementary Mathematics
PROPORTION
EXAMPLE 2
Find
the unknown value in the
proportion: (2x + 1) : 2 = (x + 2) :
5
(2x
+ 1) : 2 = (x + 2) : 5
First,
convert the colon-notation
ratios to fractions:
(2x
+ 1)/2 = (x + 2)/5
Then
solve:
5(2x
+ 1) = 2(x + 2)
10x
+ 5 = 2x + 4
8x
= 1
x
= 1/8
MERCHANDISING
What
does merchandising
cover?
·
Understand
the ordinary dating notation
for the terms of payment of
an
invoice.
·
Solve
merchandise pricing problems
involving mark ups and
markdowns.
·
Calculate
the net price of an item
after single or multiple
trade discounts.
·
Calculate
a single discount rate that
is equivalent to a series of
multiple
discounts.
·
Calculate
the amount of the cash
discount for which a
payment
qualifies.
STAKEHOLDERS
IN Merchandising
Who
are the stakeholders in
merchandising?
The
main players are:
·
Manufacturer
·
Middleman)
·
Retailer
·
Consumer
There
are discounts at all levels
in the above chain.
MIDDLEMAN
A
middle man is a person who
buys a product directly from
the manufacturer, and
then
either
sells the product at retail
prices to the public, or
sells the product at
wholesale prices
to
a distributor. There can
often be more than one
middle man when the
latter practice is
adopted.
A middle man can purchase
from the manufacturer and
then work with
another
middle
man who buys for
the distributor. The
manufacturer often views the
middle man as
the
alternative to direct
distribution.
List
price or Retail
price
List
price refers to the
manufacturer's suggested retail
pricing. It may or may not
be the price
asked
of the consumer. Much
depends on
1.
the product itself,
2.
the built-in profit
margin,
3.
Supply and demand.
A
product that is in high
demand with low availability
will sometimes sell
higher
than
the list
price,
though this is less common
than the reverse.
Virtually
all products have a
suggested retail or list
price. Resellers (middleman,
retailer) buy
products
in bulk and get a
substantial discount in order to be
able to get profit from
selling
the
product at or below list
price.
Page
141
MTH001
Elementary Mathematics
Trade
Discount
If
Let L is the list price,
then amount of trade discount is some
calculated as percentage % d of
this
price.
List price less amount of
discount is the net price. In mathematical
terms, we can write:
Amount
of discount = d × L
Where,
d = Percentage of Discount
L
= List Price
Net
Price = L Ld = L(1
d)
Net
Price = List Price
Amount of Discount
Page
142
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