Six is subtracted from a number.
The result is equal to one fourth of the sum of the number and 45 find the number .
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
⟹ (x – 6) = x + 45/4
⟹ 4(x – 6) = x + 45
⟹ 4x – 24 = x + 45
⟹ 4x – x = 45 + 24
⟹ 3x = 69
⟹ x = 69/3
⟹ x =23
Hence, the number is 23.
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Six is subtracted from a number and the resulting number is equal to one fourth of the sum of the number and 45 .
The Number .
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀
❍ Let's say that the number is a
:
⠀⠀⠀━━━ Six is subtracted from a number is equal to one fourth of the sum of the number and 45 .
[tex]\begin{gathered}\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{\bold{ \:a = 23} }} }\:\:\bigstar \\\end{gathered}[/tex]
