Chapter SH, Problem 3.5MPS

To determine

To calculate:To find the fraction of the surveyed people who listen to station WABC, where $\frac{2}{3}$ of the people are surveyed and $\frac{3}{4}$ of the surveyed people listen to station WABC.

Answer to Problem 3.5MPS

Fraction of the surveyed people who listen to station WABC $=$$1\frac{1}{8}$ .

Explanation of Solution

Given information:

  $\frac{2}{3}$ of the people are surveyed and $\frac{3}{4}$ of the surveyed people listen to station WABC.

Calculation:

Given:

  $\frac{2}{3}$ of the people are surveyed.

  $\frac{3}{4}$ of the surveyed people listen to station WABC.

Fraction of the surveyed people who listen to station WABC $=$$\frac{3}{4}$ of the surveyed people listen to station WABC/ $\frac{2}{3}$ of the people are surveyed.

Thus, Fraction of the surveyed people who listen to station WABC $=$$\frac{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

Solving further,

Fraction of the surveyed people who listen to station WABC $=$$\frac{3}{4}\times \frac{3}{2}$

Fraction of the surveyed people who listen to station WABC $=$$\frac{9}{8}$

Converting the improper fraction tomixed fraction, we have:

Thus, Fraction of the surveyed people who listen to station WABC $=$$1\frac{1}{8}$

Conclusion:

Fraction of the surveyed people who listen to station WABC $=$$1\frac{1}{8}$ .