I am helping my son with his math homework. Neither of us can make sense of this problem but we can solve all the others in the chapter. Is the answer key wrong?
The winning pitcher faced 32 batters during the game. If the opposing team had only 9 players, how many of those players did the pitcher face 4 times?
The answer key says 5.
How??
The opponents batted around three times. That accounts for $27=3(9)$ batters faced. But $32-27=5$, so only those five got a fourth turn at bat.
Is this really a "ratio problem"? I think it is. Mathematically, we perform a "division with remainder", which in some places is written
$$32\,\div\,9\,\,\,=\,\,\,3\,\,R\,\,5.$$
This can also be viewed as a clock-type arithmetic, such as shown here: What is 8 times 9 in 12-hour clock arithmetic?
Mathematicians would also talk about finite cyclic groups, link below. https://en.wikipedia.org/wiki/Cyclic_group