Video: Solving Word Problems Involving Ratios

The total number of students in the first, second and third grades at a primary school is 285 in the ratio 7 : 4 : 8. Calculate the number of students in each grade.

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Video Transcript

The total number of students in the first, second, and third grades at a primary school is 285 in the ratio seven : four : eight. Calculate the number of students in each grade.

We can share a total, in this case, 285 students, in a given ratio by following three steps. Firstly, we find the sum of the ratios. Seven plus four plus eight is equal to 19. Our second step is to divide the total by this answer. 285 divided by 19 is equal to 15. This is equal to one part or one share of the ratio.

Our final step is to multiply the value for one part by each of the ratios. 15 multiplied by seven is 105. 15 multiplied by four is equal to 60. 15 multiplied by eight is equal to 120. As the seven corresponded to the number of first graders, there are 105 students in first grade, 60 students in second grade, and 120 students in third grade. It is always worth checking our answers by adding the values to ensure this makes the total. 105 plus 60 plus 120 is equal to 285. This method works for sharing any total between any number of ratios.

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