The total amount spent on the bags was $600. Some of them cost $1 and the others $2. If the number of $1 bags bought was X and it is given that twice as many $1 bags were bought as $2 bags, the number of $2 bags bought was X/2.

The total cost of the bags in terms of X is 1*X + 2*(X/2). Equate this to 600 and solve for X.

X + X = 600

=> X = 300

The total number of bags was X + X/2 = 300 + 150 = 450

**The total number of bags bought was 450**

Let x be the number of $1 bags that we bought.

An, let y be the number of $2 bags that we bought.

So the total cost equation is:

`$1x+$2y=$600`

We may re-write this as:

`x + 2y = 600`

Since the number of $1 bags (x) is twice the number of $2 bags (y), then:

`x = 2y`

Substitute this to the total cost equation.

`x+2y=600`

`2y+2y=600`

`4y=600`

Divide both sides by 4, to isolate the y.

`(4y)/4=600/4`

`y=150`

So, we bought 150 pieces of $2 bag.

Then, substitute this to x = 2y.

`x= 2(150)=300`

And, we ordered 300 pieces of $1 bag.

Then, add the values of x and y to get the total number of bags.

`x + y = 300+150 = 450`

**Hence, we bought a total of 450 bags. **