Math CentralQuandaries & Queries


Question from Carla, a parent:

In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong.

Hi Carla,

Your answer is correct but I am not sure I follow your reasoning completely. I think however you have a much better number sense that I would expect from a student in grade 5. Using your line of reasoning I would have said

The number of boats is a multiple of 4 and also a multiple of 7 so it is a multiple of $4 \times 7 = 28.$ Is 28 the answer? One quarter of 28 is 7 and three sevenths of 7 is 3 so this would give 3 red boats. But there are 9 red boats so the number of boats must be 3 times 28 or 84. Check that 84 is correct. One quarter of 84 is 21 and three sevenths of 21 is 9 so 84 is the correct answer.

I think that the teacher expects a "thinking backwards" approach.

After the white boats are removed four sevenths of the remaining are blue so three sevenths are red. Thus three sevenths of the non-white boats is 9 boats so the number of non-white boats is 21. You know that three quarters of the boats are white so one quarter are non-white. Hence the number of boats is 4 times the number of non-white boats, that is $4 \times 21 = 84.$ Again check that 84 is correct.

I hope this helps,

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