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

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) (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.

RELATED QUESTIONS
The ratio of boys to girls at a rock concert was 7 to 6. if there were 1,092 boys how... (answered by richwmiller)

80% of the people at a concert were adults. 75% of the children at a concert were boys.... (answered by ikleyn,josmiceli)

At a concert, the ratio of adults to children is 3:8. The ratio of girls to boys is... (answered by ankor@dixie-net.com)

325 children are in a concert. 3/4 of the girls left the concert. 4/5 of the boys left... (answered by greenestamps,ikleyn)

What is the ratio of boys to girls if there are 20 boys and 10... (answered by Cromlix)

The ratio of girls to boys in a class is 9 : 7. If there are 10 more girls than boys, how (answered by ewatrrr)

In a live concert, 425 boys and 300 girls participated. Find the ratio of boys to girls. (answered by JulietG)

If the ratio of boys to girls is 3:1 and there are 4 girls, how many boys are... (answered by TimothyLamb)

The ratio of boys to girls at a local college is 3:5. If there are 275 girls, how many... (answered by Shana-D77)