Question

❤ Brainly by Brian ❤ ♥100♥


Four years ago, Alex was twice as old as Jake. Four years from now, Jake will be 3/4 of Alex's age. How old is Alex?​

Answer 1

Let Jake Age 4 years Ago=x years

Then Alex Age=2x years.

Present Age of Jake=(x+4) years

Present Age of Alex=(2x+4) years.

4 years from Now.

Jake age=(x+4+4)=x+8 years

Alex Age=(2x+4+4)=2x+8 years


Jake is Age is $\frac{3}{4}$ of Alex Age.

A/Q

$x + 8= \frac{3}{4} (2x + 8) \\ \\ \implies \: 4(x + 8) = 3(2x + 8) \\ \\ \implies 4x + 32 = 6x + 24 \\ \\ \implies 4x - 6x = 24 - 32 \\ \\\implies - 2x = -8 \\ \\ x = \frac{ - 8}{ - 2} \\ \\ x = 4$

Alex Present Age=(2x+4)

=2×4+4

=12

$\boxed{\mathbf{\huge{Alex=12\:years}}}$

Answer 2

Let the present age of Alex be x .

Four years ago , the age of Alex would be x - 4 .

Four years ago , Alex is twice than Jake .

So the age of Alex is twice than Jake .

Let Jake's age be y .

x - 4 = 2 y

⇒ ( x - 4 )/2 = y

∴ the age of Jake 4 years ago was ( x - 4 )/2 and that of Alex was x - 4 .

Now 4 years from now :

we have to add 8 both sides because 4 years from the past + 4 years in future .

Jake 4 years after will become ( x - 4 )/2 + 8 and Alex becomes x + 4 .

Given that Jake is 3/4 th of Alex's age we can now calculate the value of x :

$\frac{(x-4)}{2}+8=\frac{3}{4}(x+4)\\\\\implies \frac{x-4+16}{2}=\frac{3x+12}{4}\\\\\implies \frac{x+12}{2}=\frac{3x+12}{4}\\\\\implies 2x+24=3x+12\\\\\implies 3x-2x=24-12\\\\\implies x=12$

The present age of Alex is 12 years .

EXTRA INFO :-

The present age of Jake = 8

4 years ago it was ( 12 - 4 )/2 = 8/2 = 4 .

Currently it is 4 + 4 = 8 .