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The same number of people live on the islands Beautiful Sunrise and Gorgeous
Sunset. Beautiful Sunrise is having a fiesta today, so some people from Gorgeous
Sunset come to celebrate. Now the number of people on Beautiful Sunrise is seven
times the number of people on Gorgeous Sunset. What percent of the population of
Gorgeous Sunset is on Beautiful Sunrise now?

Sagot :

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

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