3. PAIRS OF EQUATIONS
Education is what remains when one has forgotten
everything learnt in school.
- Albert Einstein
Perfect numbers like perfect men are rare.
- Rene Des Cartes
INTRODUCTION
An equation is a statement formed by taking two
algebraic expressions equal.
eg: If expressions 4x-y and 2x+y are equal in value ie,
4x-y = 2x+y
then the algebraic statement 4x-y = 2x+y is called an
equation. The equation 4x-y = 2x+y consists of two
variables (unknowns) x and y such that each variables
used is of the first degree ( ie, power of each variable is
one)
4. Mental math and letter math
Let’s start with a problem which do can do in your head:
Three books of same price and a pen for five rupees
were bought for thirty five rupees. What is the price
of one book?
We can quickly see that the price of the three books is
thirty rupees and so the price of each is ten rupees, right?
Look at this problem:
Four chairs of the same price and a table for 3150
rupees were bought for 4950 rupees. What is the
price of a chair?
Here also we can mentally work out the steps; but for the
actual computation we need pen and paper, right?
Price of four chairs = 4950-3150 = Rs. 1800
Price of one chair = 1800/4 = Rs. 450
Now another problem
The perimeter of a rectangle is 20 centimetres; and
its length is 2 centimetres more than the breadth.
What is the length of each side?
5. Here, it is more convenient to use algebra (you can also
try otherwise). If we denote the breadth of the rectangle
by x, then using the given facts, we get
2 x + 2 = 10
and from this we find
x = 4
thus the breadth is 4 centimeters and length is 6
centimeters.
In a box, there are black and white beads. The
number of black beads is eight more than the number
of white beads; and the total number of beads is four
times the number of white beads. How many black
and how many white beads are there in the box?
Here we have to use algebra. If we denote the number of
white beads as x, then using all the given facts, we can
form the equations
X+ (x+8) = 4x
( do it!). From this we can find
2x = 8
and then
x = 4
6. thus the number o f white beads is 4 and the number of
black beads is 12
Now try the problems below on your own.
Exercise
1. When five pens were bought together , the total price
was reduced by three rupees and only seventeen
rupees had to paid. Had they been bought one by one,
how much would have been the price of each pen?
2. Four added to half of a number gives hundred. What
is the number?
3. Two persons divide hundred rupees between them
and one got ten rupees more than the other. How
much did each get?
4. A hundred rupees note was changed to ten rupee
notes and twenty rupee notes, eight notes in all. How
many tens and how many twenties?
5. Raji’s age is three times that of her brother Rajan.
After two years, Raji’s age would be two times that
of Rajan. How old are they now?
7. Answers
1. 4
2. 192
3. 45 and 55
4. Ten rupee notes = 6 and Twenty rupee notes =2
5. Rajan’s age = 2 and Raji’s age = 6
