Soru

A commercial bakery mixes three types of flour—whole wheat, rye, and oat—to create a specialty bread blend. Initially, the ratio of whole wheat flour to rye flour to oat flour by weight is $5:3:2$. The baker then adds 12 pounds of oat flour and 6 pounds of rye flour to the batch while leaving the amount of whole wheat flour unchanged. As a result, the ratio of whole wheat flour to oat flour in the new mixture becomes $1:1$. What was the total weight, in pounds, of the initial flour mixture before any additional flour was added?