Chapter 8.1, Problem 19CYU

a.

To determine

To write an equation for the number of students who drove to the destination.

Answer to Problem 19CYU

  $T=3n+7$

Explanation of Solution

Given:

Total number of students traveled, $T=14n+21$ .

Number of students who flew to the destination, $F=8n+7$ .

Concept used:

Number of students who drove to the destination, $D=T-F$ .

Calculation: Number of students who drove to the destination is given by $D=T-F.$

  $\begin{array}{l}\Rightarrow D=\left(14n+21\right)-\left(8n+7\right)\\ \Rightarrow D=14n+21-8n-7\\ \Rightarrow D=14n-8n+21-7\\ \Rightarrow D=6n+14\end{array}$

Conclusion:

Therefore, number of students who drove to the destination is modeled by the equation

  $D=6n+14$ .

b.

To determine

To find the number of students who will drive to their destination in 2027.

Answer to Problem 19CYU

  $116$

Explanation of Solution

Given:

Total number of students traveled, $T=14n+21$ .

Number of students who flew to the destination, $F=8n+7$ .

Number of students who drove to the destination, $D=6n+14$

Concept used:

Number of students who drove to the destination, $D=6n+14$

Calculation: Number of students who drove to the destination in 2010 is given by $D=6n+14.$

Number of years, $n=2027-2010$

  $=17$

  $\begin{array}{l}\Rightarrow D=6n+14\\ \Rightarrow D=6\times 17+14\\ \Rightarrow D=102+14\\ \Rightarrow D=116\end{array}$

Conclusion:

Therefore, number of students who will drive to their destination in 2027 is $116$ .

c.

To determine

To find the number of students who will drive or fly to their destination in 2030.

Answer to Problem 19CYU

  $301$

Explanation of Solution

Given:

Total number of students traveled, $T=14n+21$ .

Number of students who flew to the destination, $F=8n+7$ .

Number of students who drove to the destination, $D=6n+14$

Concept used:

Number of students who will drive or fly to their destination, $T=14n+21$

Calculation: Number of students who will drive or fly to their destination in 2030 is given by

  $T=14n+21$

Number of years, $n=2030-2010$

  $=20$

  $\begin{array}{l}\Rightarrow T=14n+21\\ \Rightarrow T=14\times 20+21\\ \Rightarrow T=280+21\\ \Rightarrow T=301\end{array}$

Conclusion:

Therefore, number of students who will drive or fly to their destination in 2030 is $301$ .