I got the correct answer, but I hesitated because I wasn’t sure we could conclude that the total number of people was 75 (25 + 50). What information/keywords in a question let us conclude that 75 is the total here? In the second screenshot below, it specifically states that “There are” x amount of animals, so I knew the number of animals for sure. However, in the third screenshot, we can’t determine the number of pens in the bag, which is why I’m a bit confused.
We cannot conclude that there are 75 total people.
- Reduce the given ratio into the smallest irreducible fraction and introduce a multiplier.\frac{Doctors}{Nurses}=\frac{25}{50}=\frac{1k}{2k}
- Notice that we can cancel the multiplier, k to get \frac{1}{2}, but we leave it as a place holder with which we can obtain all other equivalent fractions.
In other words, we can get
\frac{1k}{2k}=\frac{1}{2}~when~k~is~1,
\frac{1k}{2k}=\frac{2}{4}~when~k~is~2,
\frac{1k}{2k}=\frac{19}{38}~when~k~is~19
and
\frac{1k}{2k}=\frac{25}{50}~when~k~is~25
Basically, k which in this question represents doctors can be any positive integer and the nurses will be twice that number.
- Since we don’t know the specific number of nurses and doctors, we can use the \frac{1k}{2k} to find the total number of people. Realize that there are 1k~doctors and 2k~nurses making 3k~total~number~of~people.
- So Qa = \frac{2k}{3k}~which~simplifies~to~\frac{2}{3}
- By this too, we can tell that the total number of people (docs + nurses) will be a multiple of 3.