Let us learn the application of linear equation in maths with examples. Questions that arise in our daily life can easily be solved using mathematical operations. But usually, these problems are present in the form of word problems.

For example:

- What will be the monthly payment on my mortgage?
- How should I manage my timetable to get good marks in mathematics?
- How safe is it to invest in this new mobile?

In order to answer such questions, it is necessary to have certain pertinent information. For instance, to determine the monthly payment on a mortgage, you need to know the amount of the mortgage, the interest rate, and the time period involved.

Problems in which a question is asked and pertinent information is supplied in the form of words are called �**word problems**� or �**story problems**�.

In solving word problems we should follow these steps:

**Step 1. Understanding the problem:**

By going through the problem find out what is given and what we need to find out.

**Step 2. Decide the operation: **Now decide which fundamental operation is to be used.�����������

**Step 3. Formulating the mathematical problem:**

Convert the word problem into the equation with known and unknown quantities and the operation is decided.

**Step 4. Solve the equation:**

Solve the equation to find unknown quantities.

**Step 5. Check your answer:** Putting the values in check your answer.

**Application Of Linear Equation in Maths With Examples**

**Question: **Meena has 3 times as many two-rupee coins as she has five-rupee coins. If she has in all a sum of Rs. 77, how many coins of each denomination does she have?

**Solution:**

**Given:** Total amount = Rs. 77

**To find:** Number of each type of coins.

**Step 2. Decide operation**

Adding the number of coins will give 77.

**Step 3. Formulate the mathematical problem:**

i.e., 5x + 6x = 77

**Step 4. Solve the equation:**

5x + 6x = 77

11x = 77

Dividing by 11 both sides, we have

x=77/11

x=7

**Step 5. Check the solution.**

5x + 6x =77

11x = 77

Putting x = 7

11 (7) = 77

77 = 77

L.H.S = R.H.S

**Question: **The present age of Anu�s mother is three times the present age of Anu. After 5 years their ages will add to 66 years. Find their present ages.

**Solution:**

__Step 1. Understanding the problem:__

Let Anu�s present age be x years.

So, Anu�s mother's age will be 3x years.

**5 years later**

Anu�s age will be x + 5 years, and

Anu�s mother's age will be 3x + 5 years.

| Anu | Mother |

Present age | x | 3x |

Age 5 years later | x + 5 | 3x + 5 |

It is given that the sum of ages after 5 years is 66 years.

__Step 2. Decide operation__

So sum of their ages 5 years later will be 4x + 10 years.

| Anu | Mother | Sum |

Present age | x | 3x | 4x |

Age 5 years later | x + 5 | 3x + 5 | 4x + 10 |

__Step 3. Formulate mathematical equation__

Therefore, 4x + 10 = 66

__Step 4. ____Solve the equation__

4x + 10 = 66

4x = 66 � 10

4x = 56

Dividing 4 on both sides

x = 56/4

x = 14

Thus, Anu�s present age is x = 14 years

Anu�s Mother�s age is 3x = 3 � 14 = 42 years.

**Step 5: Verification:**

Anu�s age after 5 years = x + 5 = 14 + 5 = 19

Anu�s mother age after 5 years = 3x + 5 = 3 � 14 + 5 = 42 + 5 = 47

Sum of both Anu�s and Anu�s mother age after 5 years = 19 + 47 = 66 years.

**Read More: **

Linear Equation Definition: Reduction in Simple and Linear Form

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