Chapter 5.2, Problem 20E

To determine

To find: thenumber of tube the group rented

Answer to Problem 20E

  $11$ one person tubes and $4$ ”cooler” tubes were rented

Explanation of Solution

Given:

  $\begin{array}{l}p+c=15\\ 20p+12.5c=270\end{array}$

Calculation:

Let $p$ be the number of one person tubes and $c$ be number of “cooler” tubes

  $\begin{array}{l}p+c=15\\ 20p+12.5c=270\end{array}$

Solving for $c$ in first equation,

  $c=15-p$

Substituting the value of $c$ obtained from first equation, in equation second equation,

  $\begin{array}{l}20p+12.5(15-p)=270\\ 7.5p+187.5=270\\ p=11\end{array}$

Use the value of $p$ obtained in the solution of $c$ ,

  $c=15-p$

  $15-11$

  $4$

Verify that $(p,c)=(11,4)$ is solution to the system of equations

  $\begin{array}{l}p+c=15\\ 11+4=15\\ 15=15\\ 20p+12.5c=270\\ 20(11)+12.5(4)=270\\ 220+50=270\\ 270=270\end{array}$

Thus, $11$ one person tubes and $4$ ”cooler” tubes were rented

Conclusion:

Hence, $11$ one person tubes and $4$ ”cooler” tubes were rented