Question

if now kate is three times as old as jan, and six years ago she was six times as old as he was. How old are they both now

Answer 1

Let x be the present age of Kate

Let y be the present age of Jan

BY DATA:

At present,

Kate is three times as old as Jan

x = 3y

Let the above equation be 1

Before six years,

Let the age of Kate six years ago be x-6

Last the age of Jan six years ago be y-6

six years ago Kate was six times as old as Jan.

$x - 6 = 6 \times (y - 6) \\ \\ x - 6 = 6y - 36$

Let the above equation be 2.

Substitute equation 1 in 2.

$3y - 6 = 6y - 36 \\ \\ 36 - 6 = 6y - 3y \\ \\ 30 = 3y \\ \\ y = \frac{30}{3} \\ \\ y = 10$

The present age of Jan is 10.

Now substitute y = 10 in equation 1

$x = 3y \\ \\ x = 3 \times 10 \\ \\ x = 30$

The present age of Kate is 30.

ANSWER:

Kate is 30 years old and Jan is 10 years old at present.

Answer 2

Answer:

Given :-

• If now Kate is three times as old as Jan and six years ago she was six times as old as he was.

To Find :-

• What is the present age of Kate and Jan.

Solution :-

Let,

$\mapsto \sf \bold{Present\: age\: of\: Kate =\: x\: years}$

$\mapsto \sf \bold{Present\: age\: of\: Jan =\: y\: years}$

Now,

$\dashrightarrow$ Kate is three times as old as Jan.

$\implies \sf x =\: 3y$

$\implies \sf\bold{\purple{x =\: 3y\: ------\: (Equation\: No\: 1)}}$

$\clubsuit$ Six years ago :

$\Rightarrow$ Age of Kate = (x - 6) years

$\Rightarrow$ Age of Jan = (y - 6) years

According to the question,

$\implies \sf 6(y - 6) =\: (x - 6)$

$\implies \sf 6y - 36 =\: x - 6$

$\implies \sf \bold{\purple{6y - 36 =\: x - 6\:------\: (Equation\: No\: 2)}}$

Now, by putting the value of x in the equation no 2 we get ,

$\implies \sf 6y - 36 =\: x - 6$

$\implies \sf 6y - 36 =\: 3y - 6$

$\implies \sf 6y - 3y =\: - 6 + 36$

$\implies \sf 3y =\: 30$

$\implies \sf y =\: \dfrac{\cancel{30}}{\cancel{3}}$

$\implies \sf\bold{\pink{y =\: 10\: years}}$

Again, by putting y = 10 in the equation no 2 we get ,

$\implies \sf 6y - 36 =\: x - 6$

$\implies \sf 6(10) - 36 =\: x - 6$

$\implies \sf 60 - 36 =\: x - 6$

$\implies \sf 24 =\: x - 6$

$\implies \sf 24 + 6 =\: x$

$\implies \sf 30 =\: x$

$\implies \sf\bold{\pink{x =\: 30\: years}}$

Hence,

$\leadsto \sf\bold{\red{Present\: age\: of\: Kate =\: 30\: years}}$

$\leadsto \sf \bold{\red{Present\: age\: of\: Jan =\: 10\: years}}$

$\therefore$ The present age of Kate is 30 years and the present age of Jan is 10 years.