Question

1. prizes are to be awarded to the best pupils in each class of an elementary school. the number of students in each grade is shown in the table, and the school principal wants the number of prizes awarded in each grade to be proportional to the number of students. if there are twenty prizes, how many should go to fifth - grade students?

grade 1 2 3 4 5
students 35 38 38 33 36
3
4
5
7

Explanation:

Step1: Calculate total number of students

Add the number of students in each grade: \(35 + 38+38 + 33+36=\sum_{i = 1}^{5}n_i\)

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Step2: Find the proportion of fifth - grade students

The number of fifth - grade students \(n_5 = 36\). The proportion \(p=\frac{n_5}{\sum_{i = 1}^{5}n_i}=\frac{36}{180}\)

Step3: Calculate the number of prizes for fifth - grade

The total number of prizes \(N = 20\). The number of prizes for fifth - grade \(x=p\times N\)

$$x=\frac{36}{180}\times20=\frac{36\times20}{180}= 4$$

Answer:

4