Question

When one fourth of a number and half of the same number are added together, the result is 90. What is
that number?
a 9
b 120
c 90
d 360​

Answer 1

Answer:

option b) 120°

Step-by-step explanation:

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Answer 2

Given:-

Sum of one-fourth of the number and half of the same number is 90.

To find:-

The number.

Assumption:-

• $\sf{Let \:the \:number\: be\: x}$
• $\sf{One-fourth\:of\:number = \dfrac{x}{4}}$
• $\sf{Half\:of\:the\:number = \dfrac{x}{2}}$

Solution:-

ATQ,

$\sf{\dfrac{x}{4} + \dfrac{x}{2} = 90}$

= $\sf{\dfrac{x + 2x}{4} = 90}$

4 will be multiplied on the RHS

=> $\sf{3x = 90\times 4}$

=> $\sf{3x = 360}$

3 moves as th denominator on the RHS

=> $\sf{x = \dfrac{360}{3}}$

=> $\sf{x = 120}$

$\sf{\therefore The\:number\:is\:120}$

About the equation:-

This is a type of linear equation in one variable.

Linear equation in one variable:-

It is a type of linear equation in which only one variable is present. Eg.:- x + 4 = 1

Variables are the symbols representing a value.

Eg.:- If we take an equation x + 4 = 1

Here x is a variable which has a value. We will get the value of variable x when we solve the equation.

x + 1 = 4

=> x = 4 – 1

=> x = 3

Therefore the value of x becomes 3.