Chapter 6.2, Problem 24PPS

a.

To determine

To find: Variables, equations.

Answer to Problem 24PPS

The variables are $x$ = number of years, $p$ = number of tourists in millions in South Americans and the Caribbean , $q$ =number of tourists un millions in Middle east

Explanation of Solution

Given information:

Number of tourists in south America = $40.3$ millions

Number of tourists in middle east = $17.0$ millions

Rate of change in tourists (in millions per year) in South America = $0.8$

Rate of change in tourists (in millions per year) in middle east = $1.8$

The variables are $x$ = number of years, $p$ = number of tourists in millions in South Americans and the Caribbean , $q$ =number of tourists un millions in Middle east

South Americans and the Caribbean = $p=ax+b$

From given information

Slope = $a=0.8$ = rate of change in tourists

Initially ( $x=0$ ) , Number of tourists = $b=40.3$

Therefore

South Americans and the Caribbean tourists, $p=0.8x+40.3$

Let

Middle east tourists = $q=cx+d$

From given information

Slope = $c=1.8$ = rate of change in tourists

Initially ( $x=0$ ) , Number of tourists = $d=17.0$

Therefore

Middle east tourists, $q=1.8x+17$

b.

To determine

To find: In how many years the number of tourists in the regions to be equal.

Answer to Problem 24PPS

23.3 years

Explanation of Solution

Given information:

Number of tourists in south America = $40.3$ millions

Number of tourists in middle east = $17.0$ millions

Rate of change in tourists (in millions per year) in South America = $0.8$

Rate of change in tourists (in millions per year) in middle east = $1.8$

From given information $p=q$

  $\begin{array}{l}p=0.8x+40.3\\ q=1.8x+17\end{array}$

  $\begin{array}{l}\Rightarrow 0.8x+40.3=1.8x+17\\ \Rightarrow 1.8x-0.8x=40.3-17\\ \Rightarrow x=23.3\end{array}$

Therefore, in 23.3 years or about 23 years 4 months the number of tourists in South America and the Caribbean will be equal to number of tourists in Middle East.