x y
A(0.2 0.8)3000
B(0.5 0.5)2000
C(0.7 0.3)5000
Where A, B, C are countries, and x and y are resorts. The Matrix represents the percent of visitors.
I need to use this matrix which I have worked out to find the number of visitors who visit X (X and Y are resorts) in a given year using the numbers of visitors to both are 3000, 2000 and 5000 respectively.
Im now a bit unsure how to go forward with constructing the linear equation to use.
Would it be:
0.2x +0.8y =3000
0.5x +0.5y =2000
0.7x +0.3y =5000
I think the total to X is
.2*3000 + .5*2000 + .7*5000
X = |.2 .5 .7 | times the column
3000
2000
5000
so I would write { X Y } column=
|.2 .5 .7|
|.8 .5 .3|
times the column
3000
2000
5000
Thanks Damon, I think I was over complicating things!
Yes, you are correct. To construct the linear equation using the given matrix, you can represent the number of visitors who visit resort X with the variable 'x' and the number of visitors who visit resort Y with the variable 'y'.
Considering the given percentages of visitors from each country, you can create the following equations:
0.2x + 0.8y = 3000 (Equation 1)
0.5x + 0.5y = 2000 (Equation 2)
0.7x + 0.3y = 5000 (Equation 3)
These equations represent the allocation of visitors from each country to the two resorts. The coefficients represent the percentages of visitors from each country, and the constants on the right side represent the total number of visitors to each country.
To solve this system of equations, you can use various techniques such as substitution, elimination, or matrix methods.