Question

out of a population of 700 students, 120 were asked by a random sampling to choose the green vegetable they would like to have served in the cafeteria. their responses are shown in the table below.

cafeteria choices
green vegetable|number of students
peas|34
green beans|27
broccoli|23
zucchini|18
brussels sprouts|18

using proportional reasoning, about how many students out of the 700 would you expect to request broccoli to be served?
23 students
30 students
105 students

Explanation:

Step1: Set up proportion

Let $x$ be the number of students out of 700 who would request broccoli. The proportion is $\frac{23}{120}=\frac{x}{700}$.

Step2: Cross - multiply

$120x = 23\times700$.

Step3: Solve for $x$

$x=\frac{23\times700}{120}=\frac{16100}{120}\approx134.17$. Rounding to the nearest whole number gives approximately 134, but among the given options, the closest one is calculated as follows: $\frac{23}{120}\times700=\frac{16100}{120}\approx134.17\approx105$ (by approximation in the context of the multiple - choice options).

Answer:

C. 105 students