My brother is 4 times as old as I am. Six years from now, he will be twice as old as I will be. How old is my brother now?

Question

My brother is 4 times as old as I am. Six years from now, he will be twice as old as I will be. How old is my brother now?

I thought the answer was 18, but that was incorrect. I had x=4y and 6+2y=x. I'm not sure how to set this up.

Answer 1

$m$=age of me

$b$=age of brother

$$4m=b$$ For every $1$ year you spent, he spent $4$ years.

To make the year value equal, one needs to multiply the number of years you spent ($m$) by $4$.

$$2(4m+6)=b$$

After $6$ years, your original age of $4m$ becomes $4m+6$.

Your brother is now twice as old as you.

Now, for every $1$ year you spent, he spent $2$ years.

To make the year value equal, one needs to multiply the number of years you spent ($4m+6)$ by $2$.

Answer 2

Let $B$ be the age of the brother and $I$ be the age of you.

We have given from the problem that right now, your brother is four times older than you. This is the same as saying: $$B=4I$$

It goes on to say that in $6$ years, he will be twice the age as you. This can be represented as: $$B+6 = 2(I+6)$$

We now have two equations in two unknowns. We can solve for the variables using some basic algebra techniques. Remember the question originally asks for the value of $B$

The easiest way would be to plug in $B=4I$ to the bottom equation to get: $$4I+6=2(I+6)$$

Then just solve for $I$ to get your current age, then plug that in to the first equation to arrive at the answer.

Answer 3

$x$ = me now

$b$ = brother now

$x + 6$ = me in six years

$b+ 6$ = brother in six years.

So....

$b = 4x$

$b + 6 = 2(x +6)$.

Two linear independent equations with two unknown variables. Solve them. It's straightforward.

Answer 4

Let's start with your first equation: $x=4y$.

From this, $x$ is your brother's age now, and $y$ is your age now.

In six years, your age will be $y+6$ and your brother's age will be $x+6$.

Six years from now, if your brother will be twice as old as you will be, then $2(y+6) = x+6$.

Can you take it from here?

Spoiler:

You're solving for $x$ so substitute $y=x/4$ in the second equation: $$2((x/4)+6)=x+6$$ Solving for $x$ gives $x=12$. You can check by seeing that if $x=12$ then $y=3$. Six years from now, $x=18$, and $y=9$.

Answer 5

This is really simple. So:

My age is $M$, Bro's age is $B$.
$2M+12=B+6$

You also have another piece of information: $\;4M=B.$

Substitute that into the equation as if it was a simultaneous equation question:

$$2M+12=4M+6,$$ $$12=2M+6,$$ $$M=3.$$

Your age is 3; Your brother's age is 12.

Answer 6

If you represent x, and your brother is 4 times your age, he would be 4*x, or 4x. In 6 years, he will be twice as old, so you become x+6, and your brother is 4x+6, but he is twice as old as you, so if you were to divide your brothers current age by half, it would be x+6=4x+6/2, which you then multiply both sides by 2, to cancel out the divide by two. Its then 2x+12=4x+6, which should be easy enough to solve, and x=3 But thats not what the question is asking. Its asking for your brothers age, but since we know that hes 3, then his brother is currently 12.