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ISD 151

ISD 151. OVERVIEW OF BASIC MATHEMATICS WITH BUSINESS APPLICATIONS. Lecture 1. Lecturer : Abdul Samed Muntaka. asmuntaka.ksb@knust.edu.gh // 0205515494. Introduction. Business decisions require precision and accuracy.

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ISD 151

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  1. ISD 151 OVERVIEW OF BASIC MATHEMATICS WITH BUSINESS APPLICATIONS • Lecture 1 Lecturer: Abdul Samed Muntaka asmuntaka.ksb@knust.edu.gh // 0205515494

  2. Introduction • Business decisions require precision and accuracy. • Mathematics provides a basis for introducing precision and accuracy in business. • This course is designed to provide YOU with basic knowledge on some topics YOU must master to succeed in business today. • This topic is to help you revise some of the topics you have treated already in the SHS but this time through a business lens. • At the end of this topic, you should have refreshed your minds on such topics as: Fractions, Decimals, Percentages, Ratios, Rates, Time, Simple Equations, etc.

  3. Pretext in Business Mathematics Convert to an improper fraction: 25¾ Convert to a mixed number: 23/5 Find the least common denominator of the fractions: 5/12, 7/18, and 11/20 Mixed numbers – add: 34½ + 23¾ + 34½ + 23¾ Common factions – subtract: 17/18 – 20/27 Mixed number – multiply: 5 5/8 × 4 1/6 Common factions – divide: 25/38 ÷ 15/18 Convert the decimal 0.028 to a fraction Solve y + 12.3 = 20.5 for y

  4. Pre-test in Business Mathematics Cont’d 10. Solve 5r – 2 = 2(r + 5) for r. 11. Solve for T in the formula M = P(1 + RT) 12. Find x in the proportion: 4/9 = 36/x 13. Express as a percent: 0.7 14. Express as a decimal: 142% 15. Solve for part: 1.2% of 180 is ………………. 16. Solve for base: 135 is 15% of ………………… 17. The 5% sales tax collected by Musah was GHc780. What was the amount of the total sales?

  5. Applications Involving Fractions and Decimals • Fractions are used in business to represent quantities which cannot be represented as whole numbers. • Remember that a fraction is written in the form a/b. In this case, a is the numerator and b is the denominator. • NB: The denominator cannot be zero: Why? • Decimals on the other hand are used in business to represent quantities that cannot be represented as whole numbers in the form of whole numbers. • Decimals therefore consist of two strings of digits separated by a decimal point.

  6. Solve the following: • Cabin maker Yaw Musah needs to make a cabinet door. The cabinet drawings shows an opening 24 1/16 inches wide. Yaw wants a space of 1/8 inch on each side of the cabinet door. How wide should he make the door? Ans: 24 5/16 • The central Hotel just hired a new chef. This chef makes a hot sauce that uses 1¾ tablespoons of chili powder, but he needs to increase the recipe by 3½ times. How many table spoons of chili powder should he use? Ans:6 1/8 • Contractor Mumin has a top board that is 13/16 inch thick. Mumin wants to use wood screws to attach it to a bottom board. If a wood screw is 1½ inches long, how much of the screw will be left over to go into the bottom board? Ans: 11/16 or 0.6875

  7. 4. Accra Fabric Centre sold four pieces of wool fabric to a tailor. The pieces measure 3 ¼ yrds, 2 1/3 yrds, 1 ¾ yrds and 4 ½ yrds. How many yards of wool did the tailor purchase? 5. Issah reads meters for ECG. He walked 3.6 miles on Monday; 3.7 miles on Tuesday; 2.9 miles on Wednesday; 3.25 miles on Thursday and 3.4 miles on Friday. If Issah is paid GHc0.75p per mile, what was his total wages for the walk. 6. Four messenger service drivers need gasoline for their cars. Individually, they buy 12.4, 8.9, 13.8, and 13.9 gallons. How much did they purchase all together? If a gallon of gasoline is GHc7.20, how much did they spend in all?

  8. 7. Parker Paring Co. delivered 6.2 tons of asphalt. It used 4.7 tons for a driveway and 1.2 tons for a walkway. How much asphalt was left. 8. George Bonsu Hardware sells a large-diameter plastic pipe for GHC0.07 per foot and Cooper pipe for GHc1.02 per foot. How much will Selina save by using plastic pipe if she needs 300ft of pipe? 9. A pizza chef has 24pounds of flour on hand. He needs 3.75 pounds of flour for one large recipe of Pizza dough. How many recipes can he make with the flour on hand (round to the nearest tenth.

  9. Application of Word Problems and Equations • Word problems helps business people use a systematic approach to reduce plenty “talk” into simple computations involving addition, subtraction, multiplication and division. • They are presented in the form of conversation and students are supposed to be able to use formulae and numerical equations to solve them. • An equation on the other hand is a statement that says two expressions are equal. E.g. x + 5 = 9. Meaning that x + 5 (one situation or scenario) is equal to 9 (another situation or scenario) • Equations help business people look at different scenarios and try to equate them to make meaning out of different situations has have some thins in common.

  10. Consider the following example: • Issah owns half of a small bakery. Last week, he baked 6 cakes on Monday, 9 on Tuesday, 11 on Wednesday, 8 on Thursday and 6 on Friday. He sold all the cakes for GH¢9 each. It cost Issah GH¢5 to make each cake; the rest was profit on each cake. Issah split his profit evenly with his wife. How much did his wife receive from last week’s cakes. • Solution: • Step 1: What is requested – How much money did Issah’s wife receive? • Step 2: What process will be used: • Add the cakes baked: 6+9+11+8+6 = 40 • Subtract the cost from the sales price: GH¢9 – GH¢5 = GH¢4 • Multiply the GH¢4 profit per cake by the number of cakes sold: GH¢4 * 40 = GH¢160 • Divide the total profit by 2: GH¢160 /2 = GH¢80.00 • Issah’s wife received GH¢80.00

  11. Application of Word Problems and Equations Cont’d Summary of Steps for solving word problems Determine what is being requested Determine the process you will use to solve the problem State the answer

  12. Now look at the following: • A company orders carpeting for three offices measuring 15 sq. yrds, 15 sq. yrs and 10 sq. yrds respectively. A carpet dealer sells the carpet for GHc10 a sq. yrd and gives a Ghc50 discount when the purchase is for three or more offices. How much would the company pay to have the three offices carpeted? • Step 1: What is requested: How much money would the company pay? • Step 2: What process will be used • Determine total sq. yards for the three offices: 15 + 15 + 10 = 40 yards • Multiply the price per yard by the total yards = 40 × GHc10 = Ghc400 • Subtract the Ghc50 discount: Ghc400 – Ghc50 = 350 • Ans: GHc350

  13. Now solve these using the same approach: Maria wants to upholster three chairs. Two chairs will require 4 yards of material each; the third will require 3 yards. One material costs Ghc32 per yard; the other is Ghc24 per yard. What is the difference between the costs of the two materials for upholstering the chairs. A university student worked at a local store for Ghc10.00 an hour, as his class schedule permitted. The student worked 3 hours each Monday, Tuesday, Wednesday, and Thursday. He also worked 2 hours each Friday and 8 hours each Saturday. How many weeks did the student have to work to earn Ghc792 for a new bicycle?

  14. Equations As mentioned earlier, an equation is a statement that says two expressions are equal. Equations help business people to determine how many items to introduce into a different scenario or situation to make it what is desired. Example: Misah Co. has two warehouses are different locations. In one location, there are 450 cartons of milk and in the other, 1200 cartons. If Misah Co. wants to keep the same stock at the two locations, how many cartons should be moved between the locations to achieve the set objective. Solution: To even the two locations, (450 + 1200)/2 = 825 The location with 450 needs: 825 – 450 = 375 more cartoons. This means 375 cartons of milk have to be moved from the location with 1200 to the location with 450 to achieve the set objective.

  15. Now solve the following equations 5r – 2 = 2(r + 5) 5z + 2/3 = 2 4(y + 8) = 3(y + 14) ¾q – 1/9 = 1/3 + ¼q 3(2p – 1) = 4(2.2 – p) 9.1765y + 0.3284y = 6.65343 0.3255(1 + 7.5s) = 6.67275 1.2(2 + 3r) = 0.8(2r + 5) A company had sales of Ghc25,000 and Ghc20,000 for January and February of last year respectively. If January sales this year is Ghc30,000, what is the amount needed for February in order to equal last year’s sales for the two months

  16. Rates, Time and Distance There is usually the need in business to compute how much is done in a given amount of time at a specific speed. Generally, rate, time, and distance problems are solved with the formula: Distance = Rate × Time E.g. 1. Berki traveled at 35 miles per hour for 5 hours. How far did Berki travel? D = r * t = 35 * 5 = 175 miles Berki traveled 175 miles

  17. E. g. 2. Mary needs to type an assignment that will be 30 pages long. Each page contains 200 words. If mary can type 40 words per minute, how many minutes will it take her to complete the assignment. Solution: Distance (Total words needed) = Rate (words per minute) × Time (minutes required) Distance (Total words needed) = 30 pages * 200 words per page = 6000 words 6000 words = 40 words per minute × time (minutes needed) 6000/40 = 150 minutes Mary needs 150 minutes (or 2 hours 30 minutes) to complete the assignment.

  18. Ratios, Proportions and Percentages Ratios Ratios are needed in business because often times, we need to compare quantities. A ratio is a comparison in terms of a quotient of two number a and b usually written as a/b, a:b or a to b No matter how it is written, it is read as a to b E.g. During a 7-month league season, a football team won 25 games and lost 15 games. What is the ratio of the team’s wins to games played. Solution: The ratio required is games won/games played 25/40 = 5/8 The ratio is 5 to 8 meaning that the team won 5 out of every 8 games.

  19. Try In a major city hospital, 88 patients were in the intensive care unit. If 22 nurses were on duty in the unit, what was the ratio of nurses to patients. A bathtub contains 20 gallons of water. If the tub empties in 4 minutes, what is the rate of flow of the water per minute? In a sociology class, there are 100 females and 25 males. What is the ratio of males to the total number of students in the class?

  20. Proportions A proportion is a statement that two ratios a/b and c/d are equal, written as a/b = c/d To see if a proportion is true is to determine whether the cross products of the ratios are equal. E.g. To determine whether the proportions ½ = 4/8 are equal, we find the cross products of the ratios (1. e. 1 * 8 = 2 * 4). Since the two sides are equal, it means the proportions are equal. However, taken a proportion like 3/5 = 9/10, the cross products = (3* 10) = (5 * 9) Since the two results 30 on the left is not equal to the 45 on the right, the proportions are not equal.

  21. Try these: Suppose that you make Ghc840 for working 4 weeks in a book shop. At this rate of pay, how much money will you make in 10 weeks? Forty (40) pounds of sodium hydroxide are needed to neutralize 49 pounds of sulfuric acid. At this rate, how many pounds of sodium hydroxide are needed to neutralize 98 pounds of sulfuric acid. The scale of a map is ½in to 50 miles. How many miles correspond to 2.5in At 3pm on a sunny day, Musah, who is 1.6 meters tall had a shadow that measured 2.4 meters. A nearby tree also had a shadow that measured 10.8 meters, what is the height of the tree?

  22. Percentages In business, percentages are used to measure change from one period to another. Percentages are hundredths (i.e. part of a hundred). NB: Discuss conversion of decimals to percentage, percent to decimals, factions to percentages and percent to fractions. Example: Joslin reality sold 40% more homes this year than it did last year when it sold 135 homes. How many homes did they sell this year? This can be solved in a number of ways If what they sold last year is 100%, then it means this year they sold 140%. (140% of 135 = 189 homes) 2. We also find 40% of 135 and add the result to 135. i.e. (0.4 * 135) + 135 = 189

  23. Solve the following Peggy Johnson owns a nursery. This year she sold 195 more rose bushes than she did last year. This represents a 12% increase over the previous year. How many rose bushes did peggy’s nursery sell last year? Ken Chad is a bank teller. When he started this morning, his cash drawer had coins worth Ghc86. The coins represented only 2.5% of all the money that Ken has in his cash drawer. What was the total value of all this money? Profits were Ghc11,000 last month and Ghc10,000 the previous month. What was the rate of increase? A food importer, Fontaine’s Food Expo, imports 60% of its vinegars from France, 30% from Italy and 10% from Spain. The total value of all the vinegars that it imports is Ghc92,000. What is the value of the vinegars that are not imported from France?

  24. Thank You For enquiries and queries, please contact Abdul Samed Muntaka abusamgh@yahoo.com, 020 5515494

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