Please Help With Data Analysis Questions

Question

1.In a certain class, there are are 12 girls and 17 boys. If the average (arithmetic mean) height of the girls is g and the average (arithmetic mean) height of the boys is b, what is the average height of all of the girls and boys in the class?

2. If the average (arithmetic mean) of four consecutive odd integers is 32, what is the value of the least of the four integers?

Answer 1

Average height = (12*g + 17*b​​ ) / 29

Let the four consecutive odd integers be:

x, x+2, x+4, x+6x,

Their average is:

[x+(x+2)+(x+4)+(x+6)] / 4 = [4*x + 12] / 4 = x + 3

We’re told the average = 32:

x + 3 = 32 ⇒ x = 29