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RATIO AND PROPORTION MERCHANDISING:Punch recipe, PROPORTION

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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.
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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
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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
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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.
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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
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Table of Contents:
  1. Recommended Books:Set of Integers, SYMBOLIC REPRESENTATION
  2. Truth Tables for:DE MORGAN’S LAWS, TAUTOLOGY
  3. APPLYING LAWS OF LOGIC:TRANSLATING ENGLISH SENTENCES TO SYMBOLS
  4. BICONDITIONAL:LOGICAL EQUIVALENCE INVOLVING BICONDITIONAL
  5. BICONDITIONAL:ARGUMENT, VALID AND INVALID ARGUMENT
  6. BICONDITIONAL:TABULAR FORM, SUBSET, EQUAL SETS
  7. BICONDITIONAL:UNION, VENN DIAGRAM FOR UNION
  8. ORDERED PAIR:BINARY RELATION, BINARY RELATION
  9. REFLEXIVE RELATION:SYMMETRIC RELATION, TRANSITIVE RELATION
  10. REFLEXIVE RELATION:IRREFLEXIVE RELATION, ANTISYMMETRIC RELATION
  11. RELATIONS AND FUNCTIONS:FUNCTIONS AND NONFUNCTIONS
  12. INJECTIVE FUNCTION or ONE-TO-ONE FUNCTION:FUNCTION NOT ONTO
  13. SEQUENCE:ARITHMETIC SEQUENCE, GEOMETRIC SEQUENCE:
  14. SERIES:SUMMATION NOTATION, COMPUTING SUMMATIONS:
  15. Applications of Basic Mathematics Part 1:BASIC ARITHMETIC OPERATIONS
  16. Applications of Basic Mathematics Part 4:PERCENTAGE CHANGE
  17. Applications of Basic Mathematics Part 5:DECREASE IN RATE
  18. Applications of Basic Mathematics:NOTATIONS, ACCUMULATED VALUE
  19. Matrix and its dimension Types of matrix:TYPICAL APPLICATIONS
  20. MATRICES:Matrix Representation, ADDITION AND SUBTRACTION OF MATRICES
  21. RATIO AND PROPORTION MERCHANDISING:Punch recipe, PROPORTION
  22. WHAT IS STATISTICS?:CHARACTERISTICS OF THE SCIENCE OF STATISTICS
  23. WHAT IS STATISTICS?:COMPONENT BAR CHAR, MULTIPLE BAR CHART
  24. WHAT IS STATISTICS?:DESIRABLE PROPERTIES OF THE MODE, THE ARITHMETIC MEAN
  25. Median in Case of a Frequency Distribution of a Continuous Variable
  26. GEOMETRIC MEAN:HARMONIC MEAN, MID-QUARTILE RANGE
  27. GEOMETRIC MEAN:Number of Pupils, QUARTILE DEVIATION:
  28. GEOMETRIC MEAN:MEAN DEVIATION FOR GROUPED DATA
  29. COUNTING RULES:RULE OF PERMUTATION, RULE OF COMBINATION
  30. Definitions of Probability:MUTUALLY EXCLUSIVE EVENTS, Venn Diagram
  31. THE RELATIVE FREQUENCY DEFINITION OF PROBABILITY:ADDITION LAW
  32. THE RELATIVE FREQUENCY DEFINITION OF PROBABILITY:INDEPENDENT EVENTS