In this chapter we will solve some word problem questions related to linear equation in one variable.

To solve the questions, **you have to follow below steps**;

(a) Frame the equation after reading the question.

(b) Solve the equation and find the unknown variable.

Hence, apart from math skills, you should also posses reading comprehension skills so that you can frame the equation accurately.

To have basic understanding of solving linear equation, click the below links.

**How to solve linear equation ?****Solving linear equation using cross multiplication**

## Word Problems on Linear equation with one variable.

**Example 01**

For cleaning the garden, Sam was paid 20$. After the payment, Sam has 60$ in his wallet. Find the money in the wallet before the payment?

**Solution**

Let the **money before payment was x $**.

We know that **Sam received $20 for his services and after the payment he has 60$**.

We can say that;

Initial money + 20 = 60

x + 20 = 60

x = 60 – 20

x = 40

Hence, **Sam had 40$ before the payment.**

**Example 02**

Peter is 5 years younger than Ashley. Four years later, Ashley will be twice as old as Peter. Find their present ages?

**Solution**

Let** Ashley’s age be x**.

Then **Peter age will be x – 5.**

Age of both the person after 4 years.

Ashley = x + 4

Peter = x – 5 + 4

It is said that after 4 years, Ashley age is twice as old as Peter.**So we multiply Peter age by 2 to make it equal to Ashley’s age**.

2 . (x – 5 + 4) = x + 4

2 (x – 1) = x + 4

2x – 2 = x + 4

2x – x = 4 + 2

x = 6

Hence, **Ashley Present age is 6 years**.**Peter Present age is = 6 – 5 + 4 = 5 years**

**Example 03**

If we multiply weight of the box by 8/3, we will get 24 Kg. What is the original weight of the box.

**Solution****Let weight of the box be x kg**.

According to question, **if we multiply the box by 8/3 we will get 24 kg.**

\mathtt{x\ \times \ \frac{8}{3} =\ 24}

Solving the linear equation, we get;

\mathtt{x\ \times \ \frac{8}{3} =\ 24}\\\ \\ \mathtt{\frac{8x}{3} =\ 24}\\\ \\ \mathtt{x\ =\ \frac{24\ \times 3}{8}}\\\ \\ \mathtt{x\ =\ \frac{\mathbf{3} \ \cancel{24} \ \times 3}{\cancel{8}}}\\\ \\ \mathtt{x\ =\ 9}

Hence, **the original weight of box is 9 Kg.**

**Example 04**

When number is divided by 8, the result is 5. Find the original number.

**Solution**

Let the original number be x.

According to question, **when we divide number x by 8 we get number 5**.

\mathtt{\frac{x}{8} =\ 5}\\\ \\ \mathtt{x=\ 8\times 5}\\\ \\ \mathtt{x\ =\ 40\ }

Hence, **40 is the original number.**

**Example 05**

The sum of two consecutive multiple of 6 is 54. Find both the numbers.

**Solution**

Let the **first multiple of 6 be x**.

The other **consecutive multiple of 6 will be x + 6.**

According to question, **both the numbers will add to number 54.**

The linear equation is written as;

x + (x + 6) = 54

Solving the linear equation.

x + x + 6 = 54

2x = 54 – 6

2x = 48

x = 48 / 2

x = 24.

The two original numbers are;

x = 24

x + 6 = 24 + 6 = 30

Hence, **number 24 & 30 are the right solution**.

**Example 06**

The sum of two numbers is 15 and their difference is 7. Find the original numbers.

**Solution**

Let the **two numbers be x & y.**

It’s given that **sum of two numbers is 15**.

x + y = 15

y = 15 – x

So, the two numbers are x and (15 – x).

According to question, **the difference of these two numbers is 7.**

x – (15 – x ) = 7

x – 15 + x = 7

2x = 7 + 15

2x = 22

x = 11

So the two numbers are;

x = 11

15 – x = 15 – 11 = 4

Hence, **11 & 4 are the solution**.

**Example 07**

The angles of triangle are in ratio 1: 2: 3. Find the measure of all the angles.**Solution**

Let the **angles of triangle are x, 2x and 3x**.

We know that **sum of all angle of triangle measures 360 degree**.

x + 2x + 3x = 360

6x = 360

x = 360 / 6

x = 60 degree.

So the measure of all angles are;

x = 60 degree

2x= 2 (60) = 120 degree

3x = 3 (60) = 180 degree

Hence, **60, 120 and 180 degree is the solution.**

**Example 08**

The cost of three laptops and two printer is 1100$. If the Laptop costs 200$ more than printer, then find the price of both the items.

**Solution**

Let the **laptop price be x** and **printer price be y**.

According to question, laptop cost 200$ more than printer.

So;**Price of Laptop = 200 + price of printer**

x = 200 + y

y = x – 200

Now the **laptop price is x** and **printer price is x – 200**.

According to question, **3 Laptop and 2 printer cost 1100$**

3x + 2 (x – 200) = 1100

3x + 2x – 400 = 1100

5x = 1100 + 400

5x = 1500

x = 1500 / 5

x = 300

So;**Price of laptop ( x ) = 300$****Price of printer = 300 – 200 = 100$**