Question

hey! mates help me.helpme .help me.​

Answer 1

Answer:

My age = x = 38 years

Son's age = y = 10 years

Step-by-step explanation:

At present:

My age = x years,

Son's age = y years

Two years ago:

My age = (x-2) years

son's age = (y-2) years

$x-2 = 4\frac{1}{2}(y-2)$

$\implies x-2 = \frac{9}{2}(y-2)$

$\implies 2(x-2) = 9(y-2)$

$\implies 2x - 4 = 9y - 18$

$\implies 2x - 9y = -14 \: ---(1)$

6 years ago:

My age = ( x - 6 ) years

Son's age = ( y - 6 ) years

$x - 6 = 2(y-6)^{2}$

$\implies x - 6 = 2(y^{2}-12y+36)$

$\implies x - 6 = 2y^{2}-24y+72$

$\implies x = 2y^{2}-24y+78\:---(2)$

/* Substitute (2) in equation (1) ,we get

2(2y^{2}-24y+78) -9y = -14

=> 4y²-48y + 156-9y + 14 =0

=> 4y²-57y + 170 = 0

=> 4y² -40y -17y + 170 =0

=> 4y(y-10)-17(y-10)=0

=> (y-10)(4y-17) = 0

=> y - 10 = 0 Or 4y - 17 = 0

=> y = 10 Or y = 17/4

substitute y = 10 in equation (1), we get

2x - 9×10 = -14

=> 2x - 90 = -14

=> 2x = 90 - 14

=> 2x = 76

=> x = 76/2 = 38

Therefore.,

At present:

My age = x = 38 years

Son's age = y = 10 years

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