Application of Linear Equations -- Mr K Bhanumoorthy

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Application of Linear Equations

“Tell me and I forget 

  Teach me and I remember 

   Involve me and I learn” …………Fenjamin Franklin 

Before introducing variables, say x, y, z, a, b, c,.to form a statement of an equation, let me share few lines, how to introduce, guide lines/suggestions, to form a statement, further  an equation from the given data.

Algebra is generalized arithmetic. Few examples be given, be discussed, in brief to be conversant   with statement. At the beginning some numerical.

e.g.: 1. Kunal’s present age is 20years. What was his age before 7 years? What will be his age after /hence 5 years? The students are to be drilled to give the correct answer knowing the operation to be carried out. Answers: 13 years, 25 years. (operation; subtraction, addition)

2.In the same way, Rajan’s present age is 25 years, his father’s age is 2 times of his age. Find Rajan’s father’s present age ?  The ANSWER IS 2 × 25 = 50 YEARS. {OPERATION IS([MULTIPLICATION)

This would facilitate students, to think, and decide the kind of operation to be carried out. Let me Proceed further in solving age related questions.

 

1. The sum of present ages of father and son is 54 years.6 years ago father was 6 times age of his son. Find the present ages of son and father.

Let age of son be x years, father be y years, then, as per given data, x + y = 54, where y = 54 - x.

6 years ago, son   x - 6 years, while father was 54 -x- 6, i.e.  y = 54 -x - 6 = 48 -x years.

As per data   48 -x = 6 (x – 6), by solving we will get x = 12, y = 42, hence age of son is 12yrs, father is 42yrs.

II. 5% of what is 20?      

Let 5 % of x be equal to 20, (5/100) × x = 20, x = 20 × (100 / 5) = 400.

Hence the answer; 400.

III What % of 400 is 20.

Let us assume x % of 400=. 20, (x/ 100) × 400= 20, solving we will get the answer 5 .

Iv. The distance covered by a train in 3 hours is 180 kms Find the speed of the train. Assume train covers equal distance in equal intervals of time.

We can use the formula, Distance = speed x time. If, distance is d, speed is s, time as t then  

d=s x t or s = d / t, using the formula we get speed is 60 Km per hour. Ans: 60km / hour.

v. The sum of digits of a two-digit number is 9. If digits are reversed the number is decreased by 9. Find the number. 

  Let the number be XY, X in ten’s place, Y be in one ’s place. The sum of digits is 9, 

 X + Y = 9. ……. I. value of number is 10X + Y; as per given data, the digits are reversed, ie YX, the value of the number is 10Y+ X. But given, the number is decreased by 9.

So 10X+ Y - 9 = 10Y +X., ie 9X— 9Y = 9, so X- Y = 1…..  II, solving between I and II we get  the solution as X = 5 and Y = 4.

Hence the number is 54 the answer.

vi. There are two industries engage workers. one industry say A pays Rs 240 per hour, and the other say B pays Rs.6000.per week. They have to work for 30 hours. Which is advantage for the worker? 

For industry B: 6000 = 30 × X (X being the amount per hour), So X = Rs.200. We can easily conclude industry A is beneficial.

  

Next topic: Quadratic Equation

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Mr. K Bhanumoorthy is a retired KVS Principal and recipient of Ramanujan Award. He lives in Bengaluru.

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