[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Sofian's current age is (2x + 3) times Mastura's age.
★ Mastura's current age is (x + 5) years
★ 6 years ago, the sum of their ages is 44 years.
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The value of x.
[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
According to the question,
Present age of Mastura = (x + 5) years
Present age of Sofian = (2x + 3) (x + 5) years, i.e :
[tex] \longrightarrow \tt (2x + 3) (x + 5)[/tex]
[tex] \longrightarrow \tt 2 {x}^{2} + 10x + 3x + 15[/tex]
[tex]\longrightarrow \tt 2 {x}^{2} + 13x + 15 \: years[/tex]
Now,
Mastura's age 6 years ago = (x + 5) - 6
=> x + 5 - 6
=> x - 1
Sofian's age 6 years ago = 2x² + 13x + 15 - 6
= 2x² + 13x + 9
Using the condition provided by the question,
Mastura's age 6 years ago + Sofian's age 6 years ago = 44
[tex] \longrightarrow \tt (x - 1) + (2 {x}^{2} + 13x + 9) = 44[/tex]
[tex] \longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44[/tex]
[tex] \longrightarrow \tt 2 {x}^{2} + 14x + 8 = 44[/tex]
[tex] \longrightarrow \tt 2 {x}^{2} + 14x + 8 - 44 = 0[/tex]
[tex]\longrightarrow \tt 2 {x}^{2} + 14x - 36= 0[/tex]
• Taking "2" common.
[tex]\longrightarrow \tt 2 ({x}^{2} + 7x - 18) = 0[/tex]
[tex]\longrightarrow \tt {x}^{2} + 7x - 18 = \dfrac{0}{2} [/tex]
[tex]\longrightarrow \tt {x}^{2} + 7x - 18= 0[/tex]
• Using splitting the middle term
[tex]\longrightarrow \tt {x}^{2} + 9x - 2x - 18 = 0[/tex]
[tex]\longrightarrow \tt x(x + 9) - 2(x + 9) = 0[/tex]
[tex]\longrightarrow \tt (x + 9) (x - 2) = 0[/tex]
either [tex]\tt (x + 9) = 0 \: \: or \: \: (x - 2) = 0 [/tex]
[tex] \longrightarrow \tt x = - 9 \: \: or \: \: x = 2[/tex]
[As the age cannot be negative. So x = - 9 is rejected]
[tex] \therefore \tt \: x = \red{ 2}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Verification :}}}}}}[/tex]
According to the condition provided by the question,
• Mastura's age 6 years ago + Sofian's age 6 years ago = 44
[tex] \longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44[/tex]
Putting x = 2 we get,
[tex] \longrightarrow \tt 2 - 1 + 2( {2})^{2} + 13(2) + 9 = 44[/tex]
[tex] \longrightarrow \tt 1 + 2 \times 4 + 26+ 9 = 44[/tex]
[tex] \longrightarrow \tt 1 + 8 + 26+ 9 = 44[/tex]
[tex]\longrightarrow \tt 9 + 26+ 9 = 44[/tex]
[tex]\longrightarrow \tt 18 + 26 = 44[/tex]
[tex]\longrightarrow \tt 44 = 44[/tex]
Hence verified.
[tex]\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}[/tex]
Hope it helps you! :))
