1. Welcome To
A Session
Equations

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

3. © 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.
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4. © 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.
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1. Solution of Equations
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2. Solution of Equations
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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
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4. Solution of Equations
© Sharadindu Bikash Bhattacharjee
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13. © 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) =
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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?
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16. © 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)
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17. © 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)]
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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?
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Answer:
a) Here, earnings =E
Sales =T
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b) Earning , E = TK.20,000
Sales, T = ?
We know
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Example 8
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Thank you
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Attending the Session
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