Math, asked by vijayanchithravani, 7 hours ago

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?​

Answers

Answered by Leofangclog
46

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

Answered by ItzAshi
183

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

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