Question

in a school with 2,000 students, a random sample of 120 students were asked which fruit is their favorite. their responses are shown in the table below.

survey responses
favorite fruit|number of students
banana|23
apple|18
orange|34
peach|27
pear|18

using proportional reasoning, about how many students out of the 2,000 would you expect to select an orange as their favorite fruit?
about 34 students
about 58 students
about 283 students
about 567 students

Explanation:

Step1: Set up proportion

Let $x$ be the number of students out of 2000 who prefer orange. The proportion is $\frac{34}{120}=\frac{x}{2000}$.

Step2: Cross - multiply

$120x = 34\times2000$.

Step3: Solve for $x$

$x=\frac{34\times2000}{120}=\frac{68000}{120}\approx 567$.

Answer:

about 567 students