Page 153 - ICSE Math 7

EXERCISE 13.3

1. Solve the following by method of transposition.
(a) 17 + 3s = –4 (b) 0 = 16 + 4(m – 6) (c) 2x + 14 = 9x – 7 (d) 2(1 – x) = –12
1
x
(e) 7(x – 2) – 4(5 – x) = 1 (f) 2x – = + 3
3 3 2 2
2. Construct three linear equations starting with the given solution.

(a) m = 1 (b) n = –3 (c) q = –5 (d) x = –1
2 5

Applications of Linear Equations
We have learnt how to convert daily life situations expressed in statement form to simple equations.
We also know how to solve linear equations to find the solution of practical problems and puzzles.
The steps to solve these word problems are as follows:

Step 1: Read the problem carefully. Maths Info
Step 2: Figure out what we have to find and what is given. To verify the solution of a linear
Step 3: Assume the unknown quantity by variables. equation check whether the
given conditions are satisfied
Step 4: Form an equation and solve it to find the value of the unknown or not.
quantity.

Step 5: Verify whether the solution satisfies the equation.
Example 8: Solve the following.
(a) Maya, Madhura and Mohsina are friends studying in the same class. In a class test
in Geography, Maya got 16 out of 25 and Madhura got 20. The average score of
all the three was 19. How much did Mohsina score?
(b) The length of a rectangle is 4 cm less than thrice the width. When the length
is increased by 7 cm and the width is decreased by 2 cm, the perimeter equals
90 cm. Find the length and width of the rectangle.
Solution: (a) Maya’s score = 16
Madhura’s score = 20
Let the score of Mohsina be x.
 The average score = 19

∴ 16 + 20 + x = 19
3
⇒ 36 + x = 57
⇒ x = 57 – 36

⇒ x = 21
Hence, Mohsina’s score is 21.
(b) Let the width of the rectangle be x.
∴ Length of the rectangle = (3x – 4) cm
Increased length = (3x – 4) + 7 = (3x + 3) cm

Decreased width = (x – 2) cm
2(Length + Width) = Perimeter

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