A bag contains 8 red marbles and 40 blue marbles. If a representative sample contains 2 red
marbles, then how many blue marbles would you expect it to contain? Explain.
Because the ratio of red marbles to blue marbles is in the population, the expected number of
blue marbles is times the number of red marbles in the representative sample. There should be
blue marbles.

10 blue in the sample

Step-by-step explanation:

Representative means it  "represents" the population.  or in other words it has the same ratio.  So if half the marbles were red you would expect 2 blue marbles because then blue and red would be half and half like the population.

In this though the ratio is 8:40

If you divide this ratio you could get equivalent ratios.  Again, if it were half and half you could say it's 20:20 or 10:10 or 3:3.  You multiply both numbers in the ratio to get this.  So now, we have 8 red to 40 blue.  We want 2 red though, so what do we do to 8 to get 2?  divide by 4, so do that to 40 as well.  it becomes 2:10 so that means 10 blue marbles.    the reason of course that it represents the same ratio.  if you want to look at it as fractions 8 reds and 40 blue makes the fraction of red out of the whole thing 8/48.  this is equal to 2/12 which says 2 reds and 10 blues.

Filling in the last part of what you typed here is an appropriate fill in.

Because the ratio of red marbles to blue marbles is in the population, the expected number of  blue marbles is 5 times the number of red marbles in the representative sample. There should be 2*5 = 10  blue marbles.

So yes, this is another way of looking at it, if the ratio has a number that multiplies one into the other.  There are usually multiple ways to do math problems.