Question

The ratio of wood bats to metal bats at a sporting goods store is 2:7. After 10 metal bats are sold, the ratio of wood bats is 3:8. How many wood bats are there at the store?

Answer 1

w/m = 2/7
w/(m-10) = 3/8

clearing fractions, we have

7w = 2m
8w = 3m-30
so,

m = 7w/2
8w = 3(7w/2) - 30
16w = 21w - 60
5w = 60
w = 12
m = 42

check:
12/42 = 2/7
12/32 = 3/8
ok!