Question

when henry surveyed 45 seventh - grade students at random in the school cafeteria, he found that 3 out of 15 liked reggae music. using proportional reasoning, about how many of the 180 seventh - grade students in his school like reggae music?
about 60 seventh - grade students like reggae music.
about 12 seventh - grade students like reggae music.
about 36 seventh - grade students like reggae music.
about 108 seventh - grade students like reggae music.

Explanation:

Step1: Set up proportion

Let \(x\) be the number of students who like reggae music out of \(180\) students. The proportion is \(\frac{3}{15}=\frac{x}{180}\).

Step2: Cross - multiply

Cross - multiplying gives \(15x = 3\times180\).

Step3: Solve for \(x\)

First, calculate \(3\times180 = 540\). Then, \(x=\frac{540}{15}=36\).

Answer:

About 36 seventh - grade students like reggae music.