Chapter PS, Problem 3.3P

To determine

Which songs will record the maximum time on the CD without going over?

Answer to Problem 3.3P

Song G

Explanation of Solution

Given: The table show song and time.

  $\begin{array}{ccccccccccc}\text{Song}& A& B& C& D& E& F& G& H& I& J\\ \text{Time}& 5\text{ min}& 9\text{ min}& 4\text{ min}& 3\text{ min}& \text{3 min}& \text{4 min}& 5\text{ min}& \text{7 min}& \text{4 min}& 5\text{ min}\\ & 4\text{ s}& 10\text{ s}& 12\text{ s}& 9\text{ s}& 44\text{ s}& 30\text{ s}& 0\text{ s}& 21\text{ s}& 33\text{ s}& 58\text{ s}\end{array}$

A CD hold 35 minutes of music.

A songs which repeats maximum number of times. Time of per songs perfectly divisible by each song time.

First change song time into seconds and CD hold music time into seconds.

In 1 min = 60 seconds.

  $\begin{array}{ccccccccccc}\text{Song}& A& B& C& D& E& F& G& H& I& J\\ \text{Time}& 304\text{ s}& 550\text{ s}& 252\text{ s}& 189\text{ s}& 224\text{ s}& 270\text{ s}& 300\text{ s}& 441\text{ s}& 273\text{ s}& 358\text{ s}\\ \text{Repeated}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}& \frac{2100}{304}\\ \text{Max}& 6.9& 3.8& 8.3& 11.1& 9.3& 7.7& 7& 4.7& 7.6& 5.8\end{array}$

Clearly, song G will recoded maximum number of times without going over.