Question

The sum of kevin and kim ages is 18. in 3 years kim will be twice as old as kevin. what are their ages now?

Answer 1

Solution :-

Let :-

Present age of Kevin = x

Present age of Kim = y

After three years :-

Age of Kevin = x + 3

Age of Kim = y + 3

According to the first condition :-

$\longrightarrow \sf x+y = 18 \\\\\longrightarrow y = 18 - x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According the second condition :-

$\longrightarrow \sf 2(x+3) = y +3 \\\\\longrightarrow 2x+ 6 = y + 3 \\\\\longrightarrow 2x-y =- 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf 2x - (18-x) = -3 \\\\\longrightarrow 2x- 18 + x = -3 \\\\\longrightarrow 2x - x = -3+18 \\\\\longrightarrow \bf x = 15$

Substitute x = 21 in eq (1) :-

$\longrightarrow \sf y = 18 - 15 \\\\\longrightarrow \bf y = 3$

Present age of Kevin = 15 years

Present age of Kim = 3 years