Question

six subtracted from a number is equal to one fourth of the sum of the number and 45 find the number ​

Answer 1

✬ Number = 23 ✬

Step-by-step explanation:

Given:

• Six is subtracted from a number.
• The result is equal to one fourth of the sum of the number and 45 find the number .

To Find:

• What is the number ?

Solution: Let the number be x.

➟ Subtracting 6 from x.

➟ (x – 6) ㅤㅤㅤㅤㅤ(eqⁿ 1)

Now,

➙ One fourth of sum of the number + 45

➙ 1/4 × x + 45

➙ x + 45/4ㅤㅤㅤㅤ(eqⁿ 2)

According to the question,

• Equation 1 = 2

$\implies{\rm }$ (x – 6) = x + 45/4

$\implies{\rm }$ 4(x – 6) = x + 45

$\implies{\rm }$ 4x – 24 = x + 45

$\implies{\rm }$ 4x – x = 45 + 24

$\implies{\rm }$ 3x = 69

$\implies{\rm }$ x = 69/3

$\implies{\rm }$ x =23

Hence, the number is 23.

Answer 2

Given : Six is subtracted from a number and the resulting number is equal to one fourth of the sum of the number and 45 .

Exigency To Find : The Number .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that the number be a .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: to \: \: the \: Question \::}}$

⠀⠀⠀━━━ Six is subtracted from a number is equal to one fourth of the sum of the number and 45 .

$\qquad \dashrightarrow \sf Number \: - \: 6 \: =\: \dfrac{1}{4} th \times \bigg( Sum_{(Number \:and \:45)}\bigg) \\\\\qquad \dashrightarrow \sf Number \: - \: 6 \: =\: \dfrac{1}{4} th \times \bigg( Number \:+ \:45\bigg) \\\\\qquad \dashrightarrow \sf a \: - \: 6 \: =\: \dfrac{1}{4} \times \bigg( a + 45\bigg) \\\\\qquad \dashrightarrow \sf a \: - \: 6 \: =\: \dfrac{1}{4}\bigg( a + 45 \bigg) \\\\\qquad \dashrightarrow \sf a \: - \: 6 \: =\: \dfrac{a}{4} + \dfrac{45}{4} \\\\\qquad \dashrightarrow \sf a \: - \: 6 \: =\: \dfrac{a + 45}{4} \\\\\qquad \dashrightarrow \sf 4\bigg( a \: - \: 6 \bigg)\: =\: a + 45 \\\\\qquad \dashrightarrow \sf 4a \: - \: 24\: =\: a + 45 \\\\\qquad \dashrightarrow \sf 4a \: \: =\: a + 45 + 24\\\\\qquad \dashrightarrow \sf 4a \: \: =\: a + 69\\\\\qquad \dashrightarrow \sf 4a \:- a \: =\: 69\\\\\qquad \dashrightarrow \sf 3a \: =\: 69\\\\\qquad \dashrightarrow \sf a \: =\: \cancel {\dfrac{69}{3}}\\\\\qquad \dashrightarrow \sf a \: =\: 23\\\\\qquad \therefore\:\: \pmb{\underline{\purple{\frak{ \:a = 23} }} }\:\:\bigstar$

• Here a denotes the number which is 23 .

$\therefore \underline {\:\:\sf Hence \:,\:The \:number \: is \: \bf 23\:\:.}\:$