Respuesta :
b in terms of g is b = g - 4
Solution:
Given that At a dance party a group of boys and girls exchange dances as follows:
Let "b" represents the number of boys
Let "g" represents the number of girls
To find: find b in terms of g
one boy dances with 5 girls, a second boy dances with 6 girls, and so on, the last boy dancing with all the girls.
Set up the following sequence, a one to tone correspondence between the elements of the boy set and the girl set:
Boy number = 1, 2, 3, 4, ....., b
Girl number = 5, 6, 7, ........., b + 4
g = b + 4
b = g - 4
Method 2:
Boy number = 1, 2, 3, 4, ....., b
Girl number = 5, 6, 7, ........., b + 4
Consider the arithmetic sequence 5, 6, 7, ........., b + 4 which is also equivalent to 5,6,7, ...... g
The formula for arithmetic sequence is:
[tex]a_n = a + (n - 1)d[/tex]
Where [tex]a_n[/tex] is the nth term of sequence
a is the first term of sequence
d is the common difference between terms
Here in the sequence 5, 6, 7, ...... g
[tex]a_n = g\\\\a = 5\\\\d = 6 - 5 = 1[/tex]
Hence we get,
g = 5 + (b - 1)1
g = 5 + b - 1
g = b + 4
b = g - 4
Thus b in terms of g is found out
