How long does it take to consume the same amount of food

Question

For a group of 32 students food lasts for 45 days. For how many days will the same food last for 72 students?

Answer 1

32 students ~ 1/45 days
72 students  ~ 1/x days
x=32*45/72 = 20

Inverse proportionality

Answer 2

Think of a student as needing (precisely) one kg of noodles a day. Since the noodles will last $45$ students for $32$ days, we must have $(32)(45)$ kg of noodles. This will last $72$ students a total of $\frac{(32)(45)}{72}$ days. Calculate.

There are many other approaches, some more algebraic than others. Whatever approach you take, note that it is obvious that (under the assumption that food need for each student is fixed) the food will last $72$ students fewer than $32$ days. So after you do a calculation, do an informal reality check: if your "answer" is greater than $32$, it must be wrong.