Applications of Linear Equation

Example

What is the height of the rectangle whose area is 96 cm2 and the length is 12 cm?

Solution

Let the height of the rectangle be‘s’.

Area of rectangle = Length × Breadth

96 = l × 12

We need to divide both sides by 12 to find the solution.

\mathrm{\dfrac{96}{12}=\dfrac{12l}{12}}

l = 8

Hence the height of the rectangle is 8 cm.

Example

Find the solution of 2x−3 = 6 − x.

Solution

Step 1: Bring all the terms including variable x on LHS and the constants on the RHS.

2x + x = 6 + 3 (sign will change while changing the position of the terms)

Step 2: Solve the equation

3x = 9

Step 3: Divide both the sides by 3 to get the solution.

\mathrm{\dfrac{3x}{3}=\dfrac{9}{3}}

x = 3

Hence the solution of the equation is x = 3.

Example

Mahi’s age is four times that of her younger brother. Five years back her age was 9 times her brother’s age. Find their present ages.

Solution

Let the Mahi’s brother age = x

Mahi’s age = 4x (as her age is 4 times that of her younger brother)

Five years back her age was = 9(x – 5) which is equal to 4x – 5

9(x – 5) = 4x – 5

9x – 45 = 4x – 5

9x – 4x = – 5 + 45 (by transferring the variable and constants on different sides)

5x = 40

\mathrm{x=\dfrac{40}{5}=8}

Mahi’s brother age = x = 8 years

Mahi’s age = 4x = 4(8) = 32 years.

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