Chapter MPS, Problem 3.3MPS

(a)

To determine

To Find: Equation that represents the given situation

Answer to Problem 3.3MPS

  $\text{⇒}x\left(\$8\right)+\left(718-x\right)\left(\$3\right)=\$4269$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Total tickets sold}=718\\ \text{Total money collected}=\$4269\\ \text{Ticket cost for one adult}=\$8\\ \text{Ticket cost for one child}=\$3\end{array}$

Formula Used:

  $\text{number of adults}\left(\text{Tickets cost of one adult}\right)+\text{number of child}\left(\text{ticket cost of one child}\right)=\text{Total money collected}$

Calculation:

  $\begin{array}{l}\text{Total tickets sold for drama performance}=718\\ \text{→}\text{Let the number of adult }=x\\ \text{→}\text{Number of child}=718-x\\ \text{⇒}\text{number of adults}\left(\text{Ticket cost of one adult}\right)+\text{number of child}\left(\text{Ticket cost of one child}\right)=\text{Total money collected}\\ \text{⇒}x\left(\$8\right)+\left(718-x\right)\left(\$3\right)=\$4269\end{array}$

Conclusion:

Thus the equation for the given situation is $x\left(\$8\right)+\left(718-x\right)\left(\$3\right)=\$4269$

(b)

To determine

To Find: Number of adults and number of child attend the drama performance.

Answer to Problem 3.3MPS

  $\begin{array}{l}\text{number of child}=295\\ \text{number of adult}=423\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Total tickets sold}=718\\ \text{Total money collected}=\$4269\\ \text{Ticket cost for one adult}=\$8\\ \text{Ticket cost for one child}=\$3\end{array}$

Formula Used:

  $\text{number of adults}\left(\text{Tickets cost of one adult}\right)+\text{number of child}\left(\text{ticket cost of one child}\right)=\text{Total money collected}$

Calculation:

  $\begin{array}{l}\text{Total tickets sold for drama performance}=718\\ \text{→}\text{Let the number of adult }=x\\ \text{→}\text{Number of child}=718-x\\ \text{⇒}\text{number of adults}\left(\text{Ticket cost of one adult}\right)+\text{number of child}\left(\text{Ticket cost of one child}\right)=\text{Total money collected}\\ \text{⇒}x\left(\$8\right)+\left(718-x\right)\left(\$3\right)=\$4269\\ \text{⇒}\$8x+\$2154-\$3x=\$4269\\ \text{⇒}\$5x+\$2154=\$4269\\ \text{⇒}\$5x+\$2154-\$2154=\$4269-\$2154\left(\text{subtract both side by }\$2154\right)\\ \text{⇒}\$5x=\$2115\\ \text{⇒}x=\frac{\$2115}{\$5}\left(\text{divide both side by }\$5\right)\\ \text{⇒}x=423\\ \text{number of adult}=423\\ \text{number of child}=718-x=718-423=295\end{array}$

Conclusion:

Thus the number of adults and child attend drama prformance is $423,295$