Gabriel and Tom went shopping with the same the amount of money. After Gabriel spent 86 dollars and Tom spent 426 dollars, the rest money of Tom is 1/5 the rest money of Gabriel. How much money does Tom have at first?

Let the initial amount of money both Gabriel and Tom had be x dollars.

After spending:

- Gabriel spent 86 dollars, so his remaining money:
Remaining money of Gabriel = x - 86

- Tom spent 426 dollars, so his remaining money:
Remaining money of Tom = x - 426

According to the problem, the remaining money of Tom is 1/5 of the remaining money of Gabriel. We can set up the equation:

x - 426 = 1/5 * (x - 86)

Now, let's multiply both sides by 5 to eliminate the fraction:

5 * (x - 426) = x - 86

Distributing the 5:

5x - 2130 = x - 86

Now, let's isolate x. First, we can subtract x from both sides:

5x - x - 2130 = -86

This simplifies to:

4x - 2130 = -86

Next, let's add 2130 to both sides:

4x = 2144

Now, divide both sides by 4:

x = 536

So, the initial amount of money that Tom had is 536 dollars.