Ten people can dig five holes in three hours. if n people digging at the same rate dig m holes in d hours: 1.is n proportional to m when d=3? 2.is n proportional to d when m=5? 3.is m proportional to d when n=10?

First. get the unit rate. That is, transform "Ten people can dig five holes in three hours" into "One person digs one holes in one hour."

We can say that

(that's still for 10 people). For 1 person this rate will be 1/10th of the above, so:

So the unit rate is 5/30. We can now set up an equation expressing the number of holes "m" dug up by "n" people in "d" hours:

which is clearly linear in n and d.

Now we can answer the questions:

(1) Is n proportional to m when d=3? Yes

which shows that n is proportional to m in this case.

(2) Is n proportional to d when m=5? No

There is an inverse proportionality, therefore this is not proportional.

(3) Is m proportional to d when n=10? Yes

There is a proportional relationship between m and d.