Question

The sum of two numbers is 60. One of the number is 7 less than the
other. Find the numbers.​

Answer 1

Given :-

The sum of two numbers is 60.

One of the number is 7 less than the  other.

To Find :-

The first number.

The second number.

Analysis :-

Consider the first number as an variable. Then the other number would be 7 less than the other.

Make an equation and get the value of the variable.

Substitute the value of the variable in the second variable.

Solution :-

Let one of the number be x. Then the other one would be x - 7

Given that,

The sum of two numbers is 60.

Making an equation,

$\sf x + x - 7 = 60$

$\sf 2x - 7 = 60$

By transposing 7,

$\sf 2x = 60 + 7$

$\sf 2x=67$

Finding the value of x,

$\sf x=\dfrac{67}{2}$

$\sf x=33.5$

First number = 33.5

Second number = x - 7

= 33.7 - 7 = 26.5

Therefore, the two numbers are 33.5 and 26.5

Verification :-

First number + Second number = Sum

By substituting,

33.5 + 26.5 = 60

Hence verified!

To Note :-

An equation having one variable with one degree is called as linear equation in one variable.

A few examples are below :-

1) 2x + 3 = 8

2) 3x - 4 = 5