SOLUTION: My son and I have been trying to solve question 37 on page 380. I believe we need to establish a rate of change for both countries and then use substitution to solve. The problem I

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: My son and I have been trying to solve question 37 on page 380. I believe we need to establish a rate of change for both countries and then use substitution to solve. The problem I      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 174550This question is from textbook algebra 1
: My son and I have been trying to solve question 37 on page 380. I believe we need to establish a rate of change for both countries and then use substitution to solve. The problem I'm having is coming up with the two slopes.
Here is the question: In 2000, approximatly 40.3 million tourists visited south america and the caribbean. The number of tourists to that area had been increasing at an average rate of .8 million tourists per year. In the same year, 17 million tourists visited the middle east. The number of tourists to the middle east had been increasing at an average rate of 1.8 million tourists per year. If the trend continues, when would you expect the number of tourists to South America and the caribbean to equal the number of tourists to the middle east? This question is from textbook algebra 1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 2 trends, South American-Caribbean tourists and middle East tourists
should be plotted as straight lines with number of tourists on the
y-axis and years on the x-axis.
The key to the problem is you have the slope (rate of change)
and a point given for each type of tourist. The slope
and a point actually define a line, so you can plot both lines
and see where they meet.
Data for the year 2000 is given, so I'll call x=0 the year
2000.
In millions of tourists, y=40.3 and x=0 for S.American
tourists. The slope in millions is .8 per year
The point-slope formula is:
%28y+-+y%5B1%5D%29%2F%28x+-+x%5B1%5D%29+=+m where m is slope
%28y+-+40.3%29%2F%28x+-+0%29+=+.8
y+-+40.3+=+.8x
(1) y+=+.8x+%2B+40.3
---------------------------
And for the Middle East tourists
y+-+17%29%2F%28x+-+0%29+=+1.8
y+-+17+=+1.8x
(2) y+=+1.8x+%2B+17
Solve for x and y to find where the lines meet
Subtract (1) from (2)
0+=+x+-+23.3
x+=+23.3
Now find y
(1) y+=+.8x+%2B+40.3
y+=+.8%2A23.3+%2B+40.3
y+=+18.64+%2B+40.3
y+=+58.94
This says that if the trends continue, the tourists to
both places will be equal in 2023, and there would be
almost 59 million going to each place