The ratio of blue tacks to red tacks on the bulletin board is 3 to 5. there are 50 red tacks. how many blue tacks are on the board?

The ratio 3 to 5 (or 3:5 (or 3/5)) captures the relationship between the number of blue tacks and the number of red tacks; we have 3 blue for every 5 red. The number of tacks might change, but so long as we can group our collection up into sets of 3 blue and 5 red tacks with none left over, that relationship still holds.

Here, we have 50 red tacks. If we want our ratio to stay the same (3 to 5), we'll need to pair a set of 3 blue tacks with every set of 5 red tacks. In a group of 50, we can make 10 groups of 5 red tacks, so we'll also need 10 groups of 3 blue tacks, which gives us a total of 30 blue tacks.

The first one is 2/3the second is 1/160the third is 4/125