Question

Sofian's current age is (2x + 3) times Mastura's age. Given that Mastura's current age is (x + 5) years and 6 years ago, the sum of their ages is 44 years. Calculate the value of x.

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Answer 1

Sofian's current age = (2x + 3) * (x + 5) or 2x^{2}x

2

+ 13x + 15

Mastura's curernt age = x + 5

Sofian's age after 6 years = (2x^{2}x

2

+ 13x + 15) - 6 or 2x^{2}x

2

+ 13x + 9

Working :

= 2x^{2}x

2

+ 13x + 15 + (−6)

= (2x^{2}x

2

) + (13x) + (15+−6)

= 2x^{2}x

2

+ 13x +9

Mastura's age after 6 years = (x + 5) - 6 or x - 1

Working:

= x + 5 + (−6)

= x + (5+−6)

= x + −1

= x - 1

We know that sum of ages 6 years ago is 44.

So the equation formed is:

2x^{2}x

2

+ 13x +9 + (x -1) = 44

Solving LHS we get:

2x^{2}x

2

+ 14x + 8 = 44

2x^{2}x

2

+ 14x = 36

2x^{2}x

2

+ 14x - 36 = 0 (Subtracting 36 from both sides)

2 (x−2) (x+9) = 0 (Fourth identity)

x = 2

∴ The value of x is 2

hope it helps you

Answer 2

`{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}`

★ 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.

`{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}`

★ The value of x.

`{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}`

According to the question,

Present age of Mastura = (x + 5) years

Present age of Sofian = (2x + 3) (x + 5) years, i.e :

`\longrightarrow \tt (2x + 3) (x + 5)`

`\longrightarrow \tt 2 {x}^(2) + 10x + 3x + 15`

`\longrightarrow \tt 2 {x}^(2) + 13x + 15 \: years`

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

`\longrightarrow \tt (x - 1) + (2 {x}^(2) + 13x + 9) = 44`

`\longrightarrow \tt x - 1 + 2 {x}^(2) + 13x + 9 = 44`

`\longrightarrow \tt 2 {x}^(2) + 14x + 8 = 44`

`\longrightarrow \tt 2 {x}^(2) + 14x + 8 - 44 = 0`

`\longrightarrow \tt 2 {x}^(2) + 14x - 36= 0`

• Taking "2" common.

`\longrightarrow \tt 2 ({x}^(2) + 7x - 18) = 0`

`\longrightarrow \tt {x}^(2) + 7x - 18 = (0)/(2)`

`\longrightarrow \tt {x}^(2) + 7x - 18= 0`

• Using splitting the middle term

`\longrightarrow \tt {x}^(2) + 9x - 2x - 18 = 0`

`\longrightarrow \tt x(x + 9) - 2(x + 9) = 0`

`\longrightarrow \tt (x + 9) (x - 2) = 0`

either
`\tt (x + 9) = 0 \: \: or \: \: (x - 2) = 0`

`\longrightarrow \tt x = - 9 \: \: or \: \: x = 2`

[As the age cannot be negative. So x = - 9 is rejected]

`\therefore \tt \: x = \red{ 2}`

`{\large{\textsf{\textbf{\underline{\underline{Verification :}}}}}}`

According to the condition provided by the question,

• Mastura's age 6 years ago + Sofian's age 6 years ago = 44

`\longrightarrow \tt x - 1 + 2 {x}^(2) + 13x + 9 = 44`

Putting x = 2 we get,

`\longrightarrow \tt 2 - 1 + 2( {2})^(2) + 13(2) + 9 = 44`

`\longrightarrow \tt 1 + 2 * 4 + 26+ 9 = 44`

`\longrightarrow \tt 1 + 8 + 26+ 9 = 44`

`\longrightarrow \tt 9 + 26+ 9 = 44`

`\longrightarrow \tt 18 + 26 = 44`

`\longrightarrow \tt 44 = 44`

Hence verified.

`\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}`

Hope it helps you! :))