# Video: Solving Word Problems Involving Ratios

The ratio of the height of Michael to that of Daniel is 3 : 1 and the ratio of the height of Daniel to that of Jacob is 2 : 5. Find the ratio of the height of Michael to that of Jacob.

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### Video Transcript

The ratio of the height of Michael to that of Daniel is three to one. And the ratio of the height of Daniel to that of Jacob is two to five. Find the ratio of the height of Michael to that of Jacob.

We are told in the question that the ratio of the height of Michael to Daniel is three to one. We are also told that the ratio of the height of Daniel to Jacob is two to five. We’ve been asked to calculate the ratio of the height of Michael to Jacob. Daniel is involved in both of the ratios that we know, one part in the first ratio and two parts in the second ratio.

If we multiply the ratio three to one by two, we get the ratio six to two. Remember, with ratios, whatever you do to the left-hand side, you must do to the right-hand side. We could therefore say that the ratio of Michael’s height to Daniel’s height is six to two. We also know that the ratio of Daniel’s height to Jacob’s height is two to five. We now know that, for every two units of height of Daniel, Michael has six units and Jacob has five units. This means that the ratio of heights of Michael to Jacob must be six to five.

If the ratio of height of Michael to Daniel is three to one and Daniel to Jacob is two to five, then the ratio of height of Michael to Jacob is six to five.