Question

At a ballroom dancing lesson there were twenty-three students. Deena danced with six boys, Chloe with seven, Moira with eight and so on for all the girls up to the last girl, Anna, who danced with all the boys. How many boys were at the lesson?

Answer 1

There were 9 girls at the party and 14 boys

Answer 2

First girl, Deena danced with 6 boys.

Second girl, Chloe danced with 7 boys.

Third girl, Moira danced with 8 boys.

And so last girl, Anna danced with all boys, given is an arithmetic series as 6, 7, 8, ........, a+(n-1)d.

Let's assume number of girls are 'n'.

Last term of a.p. series would be number of boys = a+(n-1)d.

Here a=6 and d=1, so number of boys = 6+(n-1)*1 = 5+n.

Given there were 23 students.

So total students = number of girls + number of boys

23 = n + (5+n)

23 = 2n + 5

2n = 23-5 = 18

n = 9.

Hence, there were 9 girls and 14 boys.