Question

If the sum of the ages of you and your mother is 51 and their product is 540,
What are the ages of you and your mother?​

Answer 1

Answer:

Mother is 36 yrs old and Me is 15 yrs old

Step-by-step explanation:

$x + y = 51$

$x = 51 - y$

Substitute x= 51-y here:

$xy = 540$

$(51 - y)y = 540$

$51y - {y}^{2} = 540$

${y}^{2} - 51y + 540 = 0$

$(y - 36)(y - 15) = 0$

$y = 36 \: and \: y = 15$

Substitute Y=36 here:

$x = 51 - y$

$x = 51 - 36$

$x = 15$

Let X be the age of Me and Y be the age of Mother, therefore, Me is 15 yrs old and Mother is 36 yrs old

Answer 2

Step-by-step explanation:

${\Large{\mathrm{\underline{\red{Question :-}}}}}$

If the sum of the ages of you and your mother is 51 and their product is 540, what are the ages of you and your mother ?

${\Large{\mathrm{\underline{\red{Solution :-}}}}}$

Let's take my age be x and my mother age be y

According to question,

${\bold{\sf{: \: ⟹ \: \: \: \: \: x \: + \: y \: = 51}}}{\bold{\bf{\orange{ \: \: - - - - Equation \: 1}}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: xy \: = \: 540}}}{\bold{\bf{\orange{ \: - - - - Equation \: 2}}}}$

Through Equation 1 we can get the value of x,

$: \: ⟹ \: \: \: \: \: {\bold{\sf{\fbox{\pink{x \: = \: 51 \: - \: y}}}}}$

Substitute the value of x in Equation 2

${\bold{\sf{: \: ⟹ \: \: \: \: \: (51 \: - \: y) \: y \: = \: 540}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 51y \: - \: y² \: = \: 540}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: y² \: - \: 51y \: + \: 540 \: = \: 0}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: y² \: - \: (36y \: + \: 15y) \: + \: 540 \: = \: 0}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: y² \: - \: 36y \: - \: 15y \: + \: 540 \: = \: 0}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: y( y \: - \: 36) \: - \: 15(y \: - \: 36) \: = \: 0}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: ( y \: - \: 36) \: (y \: - \: 15) \: = \: 0}}}$

Now we have two values of y,

y = 36 or y = 15

If we put (y = 36) in Equation 1 we get

${\bold{\sf{: \: ⟹ \: \: \: \: \: x \: + \: 36 \: = \: 51}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: x \: = \: 51 \: - \: 36}}}$

$: \: ⟹ \: \: \: \: \: {\bold{\sf{\fbox{\pink{ x \: = \: 15}}}}}$

Hence the daughter age is 15 years and the mother age is 36 years