Danny collects bottle caps and wrappers. He found 22 bottle caps and 30 wrappers at the park. Now he has 17 bottle caps and 57 wrappers in his collection. How many wrappers did danny have at first?

We are given that:
$$x_1 = \frac{1}{3}x_0$$
$$x_2 = \frac{1}{3}x_1$$
$$x_3 = \frac{1}{3}x_2$$

We can rewrite this using exponentiation:
$$x_1 = \frac{1}{3}x_0$$
$$x_2 = \frac{1}{3^2}x_0$$
$$x_3 = \frac{1}{3^3}x_0$$

We want to find $x_0$, so we can solve for it:
$$x_0 = 3x_1$$
$$x_0 = 3^2x_2$$
$$x_0 = 3^3x_3$$

Now we can plug in the values we are given:
$$x_0 = 3(20)$$
$$x_0 = 3^2(10)$$
$$x_0 = 3^3(5)$$

We can use the fact that $x_0$ is the same in all three equations to solve for it:
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