Respuesta :
Using the percentage concept, it is found that 75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.
What is a percentage?
The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, we have that:
- We consider that the population of both Beautiful Sunrise and Gorgeous Sunset islands is of x.
- There is a fiesta at Beautiful Sunrise, and a number a of people from Gorgeous Sunset are coming, hence, there will be x + a people at Beautiful Sunrise and x - a people t Gorgeous Sunset.
The percentage of people from Gorgeous Sunset is on Beautiful Sunrise now is:
[tex]P = \frac{a}{x} \times 100\%[/tex]
Now the number of people on Beautiful Sunrise is seven times the number of people on Gorgeous Sunset, hence:
[tex]\frac{x + a}{x - a} = 7[/tex]
We can find a as a function of x to find the percentage:
[tex]\frac{x + a}{x - a} = 7[/tex]
[tex]7(x - a) = x + a[/tex]
[tex]7x - 7a = x + a[/tex]
[tex]8a = 6x[/tex]
[tex]a = \frac{3x}{4}[/tex]
Then, the percentage is:
[tex]P = \frac{a}{x} \times 100\%[/tex]
[tex]P = \frac{\frac{3x}{4}}{x} \times 100\%[/tex]
[tex]P = \frac{3}{4} \times 100\%[/tex]
[tex]P = 75\%[/tex]
75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.
You can learn more about the percentage concept at https://brainly.com/question/10491646
