After 14 boys leave a concert, the ratio of boys to girls is 3 : 10. if there are
p girls at the concert, write an algebraic expression for the number of boys at
the beginning of the concert in terms of p.

Let total number of boys be  b.

ratio of boys after 14 boys leave is

      (b - 14) / p = 3 / 10

  =>     3 p = 10 b - 140

      =>  10 b = 3 p + 140

      = >  b = 0.3 p + 14

The algebraic expression for the number of boys at  the beginning of the concert in terms of p is n = 0.3p + 14

Solution:

Let the number of boys at the starting of the concert be “n”

And when 14 boys leave the concert, the remaining number of boys are (n-14)

According to question, the number of girls are represented by “p”

Also after 14 boys leave a concert, the ratio of boys to girls is 3 : 10

So we can frame a expression as follows:

The above equation n = 0.3p + 14 represents  the  number of boys at the beginning of the concert in terms of p

its a straight line parallel to the time axis