This is the question:
At The Crispy Critter’s Head Shop and Patchouli Emporium along with their dried up weeds, sunflower seeds and astrological postcards they sell an herbal tea blend. By weight, Type I herbal tea is $30\%$ peppermint, $40\%$ rose hips and $30\%$ chamomile, Type II has percents $40\%$, $20\%$ and $40\%$, respectively, and Type III has percents $35\%$, $30\%$ and $35\%$, respectively. How much of each Type of tea is needed to make $2$ pounds of a new blend of tea that is equal parts peppermint, rose hips and chamomile?
So the variables are the mass of each type of tea; type I's mass$=x$, type II's mass$=y$, type III's mass$=z$. Since we're about to make a blend of tea that's $2$ pounds in mass, then
$$x+y+z=2$$
Neat. But I'm stuck at this point. I don't know how to make use of that last part:"$2$ pounds of a new blend of tea that is equal parts peppermint, rose hips and chamomile". I know this means that our new blend of tea's composition will have equal parts but how do I make use of this?
With Ross Milikan's answer, this is what I can gather so far from my visual illustration. 
Your new type IV tea has equal parts of each, so $\frac 23$ pound of each component. If you use $x$ pounds of type I tea, you get $0.3x$ pounds of peppermint. You can write three equations similar to the one you did, one for each component. Then solve the three equations.