Welcome To A Session Equations

Business Mathematics Eleventh Edition BY D.C. Sancheti  V.K. Kapoor Chapter 8 Equations PowerPoint Presentation by S. B. Bhattacharjee

© Sharadindu Bikash Bhattacharjee An equation of the type ax+by+c = 0 is a linear equation. It shows relation between two algebraic expressions with the sign of equality (=) An equation holds true for particular value or values of the variable/ variables Example 9x+3 = 8x+5 holds true only for x= 2, and not for any other value. To find the value of a single variable, only one equation is needed. In order to find the values of two variables, two equations are necessary. Accordingly, three equations are needed to find the values of three variables, and so on. There are various types of equations viz. Linear quadratic equation, Cubic equation etc. Continued… © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee 1. Linear Equation An equation having degree 1 is called a linear equation. 7x+9=0 is a first degree or linear equation 2. Quadratic Equation An equation having degree 2 is called a quadratic equation. Example: (i) and (ii) are quadratic equations 3. Cubic Equation An equation having degree 3 is called a cubic equation. x3+3x2+4x+7= 0 is a cubic equation 4. Degree of an equation The highest power of the variable in any equation is the degree of the equation. © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee 1. Solution of Equations Continued… © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee 2. Solution of Equations © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee 3. Solution of Equations 3x- 5y = 2 ………….(1) xy = 8 …………(2) From equation (1) 3x = 2+ 5y Putting this value of x in equation (2), we have Continued…. © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee Continued… © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee 4. Solution of Equations © Sharadindu Bikash Bhattacharjee Continued…

© Sharadindu Bikash Bhattacharjee Continued….. © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee 5. Solution of Equations x2+xy+xz = 45……………….(1) y2+yz+yx = 75………………(2) z2+zx+zy = 105 …………….. (3) The above equations can be written as x (x+y+z) = 45……………(4) y (x+y+z) = 75……………..(5) z (x+y+z) = 105……………(6) Adding these equations, we have x (x+y+z) + y (x+y+z) +z(x+y+z) = 45+75+105 Continued…. © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee An executive is to receive compensation, B, amounting to x per cent of his company’s net profit after taxes. Taxes amount to y percent of net profits after deduction of the executive’s compensation a) letting P represent net profits before taxes, complete the following formula: B= x [ P-? (?-?) ] b) If the executive receives 25 per cent of net profits after, and taxes amount to 52 per cent of net profits after deduction of the executive’s compensation, how much must net profits before taxes be if the executive is to receive Tk.50,000? Continued… © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee Answer: a) Net profit = P before taxes Compensation, B = x of (net profit after taxes) = x of (net profit – taxes) = x(P –T ) ………..(1) where T = Tax Again, Tax, T = y of (net profit after deduction of executive’s compensation) = y of ( net profit – B) = y (P –B) Now, from (1), B = X (P-T) = X [P -y (P - B) ]…………….. (1) Continued…. © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee b) We know, B = x [P - y (P - B) ] Here, B = 50,000 x = 25 % = Putting these values in the above equation, we have 50,000 = 0.25 [P – 0.52 (P – 50,000)] Continued….. © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee Example : 7 A salesman’s earnings, E amount to 20 per cent of his total sales, T plus a bonus of per cent of any amount he sells in excess of TK 50, 000 a) Write an equation relating earnings to sales if sales exceed TK. 50,000. b) What must the man’s sales be if he is to earn TK.20,000? c) How much must he sell if his earnings are to be 25 per cent of total sales? Continued… © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee Answer: a) Here, earnings =E Sales =T © Sharadindu Bikash Bhattacharjee Continued…

© Sharadindu Bikash Bhattacharjee b) Earning , E = TK.20,000 Sales, T = ? We know © Sharadindu Bikash Bhattacharjee Continued…

© Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee Example 8 © Sharadindu Bikash Bhattacharjee

© Sharadindu Bikash Bhattacharjee Thank you For Attending the Session © Sharadindu Bikash Bhattacharjee