Chapter 6.2, Problem 5LC

To determine

To determine how many singing and comedy acts are in the show.

Answer to Problem 5LC

Number of singing acts = 7

Number of comedy acts = 5

Explanation of Solution

Given :

In a talent show of singing and comedy acts, singing acts are 5 minutes long and comedy acts are 3 minutes long. The show has 12 acts and lasts 50 minutes.

Calculation :

Let the number of singing acts to be $\text{'}x\text{'}$

Let the number of comedy acts to be $\text{'}y\text{'}$

Since, the show has 12 acts in total.

Hence, $x+y=12$ ………………...(i)

Also, each singing acts is 5 minutes long and each comedy act is 3 minutes long.

And, the overall show is 50 minutes long.

Thus, $5x+3y=50$ ………………..(ii)

Equation (i) can also be written as $y=12-x$

Substituting this in equation (ii)

  $\begin{array}{l}\Rightarrow 5x+3\left(12-x\right)=50\\ \Rightarrow 5x+36-3x=50\\ \Rightarrow 2x=50-36\\ \Rightarrow 2x=14\\ \Rightarrow x=7\end{array}$

Since, $y=12-x$

  $\begin{array}{l}\Rightarrow y=12-7\\ \Rightarrow y=5\end{array}$

Conclusion :

Hence, the number of singing acts will be ‘7’

And, the number of comedy acts will be ‘5’