Jack is twice as old as he was 5 years ago. His mother was then six times as old as he was. She is now 35 years old.

how old is jack?

5 yrs ago Jack was x years old

5 years ago his mom was 6x

now his mom is 6x+5
and now Jack is x+5

6x+5 = 35
6x = 30
x = 5

Jack is now 10

check:
5 yrs ago: Jack was 5, his mom was 6(5) = 30
now: Jack is 10, his mom is 6(5) + 5 = 35

To find Jack's age, we will first determine his age five years ago, and then double that to find his current age. Let's work through it step by step.

Let's assume Jack's current age is x. So, according to the problem, we can write the equation:

x = 2 * (x - 5)

Now, let's simplify the equation:

x = 2x - 10

To isolate x, we'll move the 2x term to the other side:

x - 2x = -10

Simplifying further, we have:

-1x = -10

Since negative signs cancel out, we have:

x = 10

Now we know Jack's age is 10 years old.