Bread Production Ratios

A bakery produces different types of bread, including sourdough, whole grain, and rye. The ratio of sourdough to whole grain bread is 3:2, and the ratio of whole grain to rye bread is 4:5. If the bakery produces a total of 120 loaves of bread, how many loaves of sourdough bread does the bakery produce?

Let the number of loaves of sourdough bread be represented by $s$, the number of loaves of whole grain bread by $w$, and the number of loaves of rye bread by $r$. Based on the given ratios, you can establish the following relationships:

$\f\frac{s}{w} = \f\frac{3}{2}$ and $\f\frac{w}{r} = \f\frac{4}{5}$.

Additionally, the total number of loaves satisfies:

$s + w + r = 120$.