Question

Emory is 27 year younger than his father seven years. Hence his father age will be three years less than 2.5 times his age. What is Emory present age???

Answer 1

Given :

• Emory is 27 year younger than his father.
• Seven years hence his father age will be three years less than 2.5 times his age.

To Find :

• Present age of Emory

Solution :

Let the present age of Father be y.

Let the present age of Emory be x.

Case 1 :

Emory (x) is 27 years younger than his father (y).

Equation :

$\sf{x=y-27\:\:\:(1)}$

Case 2 :

Age of Father seven year hence (y+7) will be 3 less than 2.5 times his (Emory) age (x+7)

Equation :

$\longrightarrow$ $\sf{y+7=2.5(x+7)-3}$

$\longrightarrow$ $\sf{y+7=2.5x+17.5-3}$

$\longrightarrow$ $\sf{y+7=2.5x+14.5}$

$\longrightarrow$ $\sf{2.5x+14.5=y+7}$

$\longrightarrow$ $\sf{2.5x-y=7-14.5}$

$\longrightarrow$ $\sf{2.5x-y=-7.5}$

$\longrightarrow$ $\sf{2.5(y-27) -y=-7.5}$

$\longrightarrow$ $\sf{2.5y-67.5-y=-7.5}$

$\longrightarrow$ $\sf{2.5y-y=-7.5+67.5}$

$\longrightarrow$ $\sf{1.5y=60}$

$\longrightarrow$ $\sf{y=\dfrac{60}{1.5}}$

$\longrightarrow$ $\sf{y=\dfrac{60\:\times\:10}{1.5\:\times\:10}}$

$\longrightarrow$ $\sf{y=\cancel\dfrac{600}{15}}$

$\longrightarrow$ $\sf{y=40}$

Substitute, y = 40 in equation (1),

$\longrightarrow$ $\sf{x=y-27}$

$\longrightarrow$ $\sf{x=y-27}$

$\longrightarrow$ $\sf{x=40-27}$

$\longrightarrow$ $\sf{x=13}$

$\large{\boxed{\sf{\purple{Present\:age\:of\:Emory\:=\:x\:=\:13\:years}}}}$

Answer 2

AnswEr:

present age of Emory is 13 years.

ExplanaTion:

Case 1 :

Let the present age of Emory be x years.

Let the present age of Father be y years.

$\sf{x\:=\:y\:-\:27\:\:\:(1)}$

Case 2 :

Age 7 years hence,

$\mapsto$ Father = (y +7) years

$\mapsto$ Emory = (x+7) years

Equation :

$\sf{y+7=2.5(x+7)-3}$

$\mapsto$ $\sf{y+7=2.5x+17.5-3}$

$\mapsto$ $\sf{y+7=2.5x+14.5}$

$\mapsto$ $\sf{y+7=2.5(y-27) +14.5}$

$\mapsto$ $\sf{y+7=2.5y-67.5+14.5}$

$\mapsto$ $\sf{y-2. 5y=-67.5+14.5-7}$

$\mapsto$ $\sf{1.5y=-67.5+7.5}$

$\mapsto$ $\sf{-1.5y=-60}$

$\mapsto$ $\sf{y=\dfrac{-60}{-1.5}}$

$\mapsto$ $\sf{y=\cancel{\dfrac{-60}{-1.5}}}$

$\mapsto$ $\sf{y=40}$

Substitute, y = 40 in equation (1),

$\mapsto$ $\sf{x=y-27}$

$\mapsto$ $\sf{x=40-27}$

$\mapsto$ $\sf{x=13}$

Hence, present age of Emory is 13 years.