SOLUTION: 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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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       Log On


   

Question 1000880: 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 by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
b = number of boys.
p = number of girls.

(b-14)/p = 3/10

multiply both sides of this equation by p to get:

b-14 = 3/10 * p

add 14 to both sides of this equation to get:

b = 3/10 * p + 14

that's your solution.

to confirm the solution is correct, pick any value for p and then xolve for b.

assume p = 10.

b = 3/10 * p + 14 which becomes:
b = 3/10 * 10 + 14 which becomes:
b = 3 + 14 which becomes:
b = 17.

the number of boys before 14 left was 17.
the number of boys after 14 left was 3
the number of girls is 10.
the ratio of boys to girls after 14 boys left is 3/10.

checks out ok.

the equation is b = 3/10 * p + 14

your solution is:

the expression for the number of boys at the beginning of the concert in terms of p is 3/10 * p + 14

this is a bit of semantics but there is a difference between an equation and an expression.

an equation indicates equality between expressions.

an expression is just one side of an equation.