How many of each group attended the festival?

Question

10,483 people attended a rock festival. If there were 811 more boys than girls, and 2,481 fewer adults over 50 years of age than there were girls, how many of each group attended the festival?

Answer 1

b + g + a = 10,483

g = number of girls

b = g + 811

a = g - 2481

 

(g + 811) + g + (g - 2481) = 10,483

3g - 1670 = 10,483

3g - 1670 + 1670 = 10,483 + 1670

3g = 12,153

3g/3 = 12,153/3

g = 4051

 

b = 4051 + 811

b = 4862

 

a = 4051 - 2481

a = 1570