Question

Able, Ben and Cal each played a game.

Able's score was six times Ben's score.
Cal's score was a third of Able's score.
Write down the ratio of Able's score to Ben's score to Cal's score.
Write the ratios in their simplest form.

Answer 1

6:1:2

Explanation:

Let a = Able's score, b = Ben's score, and c = Cal's score.

Since

Able's score was 6 times Ben's score, that means a = 6b.

Cal's score was a third of Able's score, so that means c = a/3. And since a = 6b, that means c = 6b / 3 = 2b.

Thus, the ratio of Able's score to Ben's score to Cal's score, a:b:c, is 6:1:2, because c is twice as much as b and a is 6 times as much as b.