Rebecca is twice as old as Rachel. Rachel is three years older than Jonah. Four years ago, Rachel was twice Jonah's age. How old is Rachel now?

Answer 1

First, let's define our variables and the relationships between them.

Let x = Rebecca's age, y = Rachel's age, z = Jonah's age

If Rebecca is twice as old as Rachel,

then x = 2y.

If Rachel is three years older than Jonah,

then y = z + 3.

If four years ago Rachel was twice Jonah's age, we need to account for that time on both sides of the equation.

Assuming y = Rachel's age now

then y- 4 = Rachel's age four years ago

Jonah's age four years ago would be z - 4.

Then, twice Jonah's age fours years ago would be:

2(z - 4).

Since we know that four years ago, Rachel was twice Jonah's age:

y - 4 = 2(z - 4)

Yet, we can't solve this equation with two variables. But, we can use substitution so that we're only in terms of y, since we're solving for Rachel's age.

Since we know y = z + 3, we can solve for z in terms of y.

By subtracting 3 from both sides, we get

y = z + 3

-3 - 3

y - 3 = z

Now let's substitute in y - 3 for z and solve.

y - 4 = 2(z - 4)

y - 4 = 2(y - 3 - 4)

y - 4 = 2(y - 7)

y - 4 = 2y - 14

-y -y

-4 = y - 14

+14 +14

10 = y

Thus, Rachel is now 10 years old.