Chapter 8.1, Problem 44PPS

a.

To determine

To write a function for the total number of dogs and cats adopted.

Answer to Problem 44PPS

  $T=3n+7$

Explanation of Solution

Given:

Number of dogs adopted in 2006, $D=2n+3$ .

Number of cats adopted in 2006, $C=n+4$ .

Concept used:

Total number of dogs and cats adopted, $T=D+C$ .

Calculation: Total number of dogs and cats adopted is given by $T=D+C.$

  $\begin{array}{l}\Rightarrow T=\left(2n+3\right)+\left(n+4\right)\\ \Rightarrow T=2n+3+n+4\\ \Rightarrow T=2n+n+3+4\\ \Rightarrow T=3n+7\end{array}$

Conclusion:

Therefore, total number of dogs and cats adopted is modeled by the equation $T=3n+7$ .

b.

To determine

To find the number of dogs and cats adopted in 2020.

Answer to Problem 44PPS

  $49$

Explanation of Solution

Given:

Number of dogs adopted in 2006, $D=2n+3$ .

Number of cats adopted in 2006, $C=n+4$ .

Total number of dogs and cats adopted in 2006, $T=3n+7$ .

Concept used:

Total number of dogs and cats adopted, $T=3n+7$ .

Calculation: Number of dogs and cats adopted in 2006 is given by$T=3n+7$

Number of years, $n=2020-2006$

         $=14$

  $\begin{array}{l}\Rightarrow T=3n+7\\ \Rightarrow T=3\times 14+7\\ \Rightarrow T=42+7\\ \Rightarrow T=49\end{array}$

Conclusion:

Therefore, the number of dogs and cats to be adopted in the year 2020 is $49$ .