Ratios of Children

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At a certain school, the ratio of the number of five-year-old's to the number of nine-year-old's is 12 to 5, and the ratio of the number of four-year-old's to the number of five-year old's is 3 to 4. If the ratio of the number of eight-year-old's to the number of nine-year-old's is 3 to 2, what is the ratio of the number of four-year-old's to the number of eight-year-old's?

Review: Ratios of Children


Explanation

Since we have more than two parts in the overall ratio here, a table is useful:



The various two-part relationships are written on different rows because they have not yet been related to each other. We can relate them through multiples. For example, by tripling the 4 in the second row and comparing with the first row, we can see that the top-left-most entry should be 9.

To combine the first row and the third row, we need to relate them based on the last column, which we can do by converting both into the common multiple of 10. We can write the multiple of the first row as a new row and fill in the missing multiple from the third row:



Therefore, the ratio of four-year-old's to eight-year-old's is 18 to 15, orto .

The correct answer is (D).


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