if there are 3 nurses to every 15 patients, that means there is 1 nurse to every 5 patients since we can divide by 3 to simplify the ratio.
in order to find how many nurses would care for 37 patients, we can divide by 5.
37/5 = 7.4 nurses.
however, we cannot have .4 of a nurse, so you can either say 7 nurses or 8 nurses, but 7.4 rounds down to 7.