Sharon bought a mixture of nuts that was made up of pecans, walnuts and cashews in a ratio by weight of $2:3:1$, respectively. If she bought $9$ pounds of nuts, how many pounds of walnuts were in the mixture? Express your answer as a decimal to the nearest tenth.
To find the pounds of walnuts, I need to figure out what fraction of the mixture they make up. I can do this by adding up the parts of the ratio: $2+3+1 = 6$. This means that the walnuts are $\frac{3}{6} = \frac{1}{2}$ of the mixture. To find the pounds of walnuts, I need to multiply this fraction by the total weight of the mixture, which is $9$ pounds. So the pounds of walnuts are $\frac{1}{2} \times 9 = 4.5$. 