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Example 8: 7 added to a number gives 9. Find the number.

Solution: Let the required number be x.
According to the statement, 7 added to x = x + 7
Steps to solve the word problems:
Given that 7 added to required number gives 9. • Read the word problem carefully.

Therefore, x + 7 = 9 • Identify what has been given and what we
have to find.
Subtracting 7 on both the sides, we get,
• Assume the unknown quantity by a variable
x + 7 – 7 = 9 – 7 such as x, y, etc.
x = 2 • Next, form an equation and solve it.
• At last, check whether the solution satisfies
Thus, the required number is 2. the equation.
Verification: Putting x = 2 in LHS of the equation.

LHS = x + 7 = 2 + 7 = 9 = RHS.
Example 9: What is the number when multiplied by 12 gives 96?
Solution: Let the required number be x. According to the statement, 12 multiplied by x = 12x

Given that 12 multiplied by the required number gives 96.
Therefore, 12x = 96

Dividing on both sides by 12, we get
12x 96
=
12 12

x = 8
Thus, the required number is 8.
Example 10: The sum of four consecutive odd numbers is 56. Find the numbers.

Solution: Let x, x + 2, x + 4 and x + 6 be the four consecutive odd numbers.
According to given statement,

x + x + 2 + x + 4 + x + 6 = 56
⇒ 4x + 12 = 56 create and solve
⇒ 4x = 56 – 12 = 44 Describe and solve a real-

44 life situation for the equation
⇒ x = = 11 2x + 12 = 64.
4
Thus, the required numbers are 11, 13, 15 and 17.

Example 11: The length of a rectangular plot exceeds its breadth by 9 m. If the perimeter of the
plot is 154 m, find the dimensions of the plot.
Solution: Let the breadth of the rectangular plot be x m.
\ The length of the rectangular plot = (x + 9) m

We have, perimeter of a rectangular plot = 2(l + b)
= 2{(x + 9) + x} m = 2(2x + 9) m

= (4x + 18) m

139 Simple Equations