4576 people attended a carnival. There were 3 times more children than adults.(a) Find the number of children who attended the carnival. (b) If there were 512 more girls than boys, how many girls attended the carnival?

(a) Let's denote the number of adults as "a". According to the problem, there are 3 times more children than adults, so we can denote the number of children as "3a". The total number of people who attended the carnival is the sum of adults and children, so we have the equation:

a + 3a = 4576

Solving this equation gives us:

4a = 4576 a = 4576 / 4 a = 1144

So, there were 1144 adults at the carnival. Since there are 3 times more children than adults, there were 3 * 1144 = 3432 children at the carnival.

(b) Let's denote the number of boys as "b". According to the problem, there were 512 more girls than boys, so we can denote the number of girls as "b + 512". The total number of children is the sum of boys and girls, so we have the equation:

b + (b + 512) = 3432

Solving this equation gives us:

2b + 512 = 3432 2b = 3432 - 512 2b = 2920 b = 2920 / 2 b = 1460

So, there were 1460 boys at the carnival. Since there were 512 more girls than boys, there were 1460 + 512 = 1972 girls at the carnival.