Question

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.

Answer 1

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:

`\begin{array}{l}{(n-14): p=3: 10} \\\\ {(n-14)/(p)=(3)/(10)} \\\\ {n-14=(3 p)/(10)} \\\\ {n-14=0.3 p} \\\\ {n=0.3 p+14}\end{array}`

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

Answer 2

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