After 14 boys leave the concert, the ratio of boys to girls is 3 to 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 boys:girls=3X:10X
but no. of girls is given, 10X=P
X=P/10
no.of boys=3X
3(P/10)=3P/10
but already 14 left from the concert
=14+(3P/10)
Let's start by setting up a proportion to relate the number of boys to the number of girls at the concert.
If after 14 boys leave the concert, the ratio of boys to girls is 3 to 10, we can write:
(Number of boys at the beginning) / (Number of girls at the beginning) = 3/10
Let's denote the number of boys at the beginning as "b". The number of girls at the beginning will be "p" since we are given "p" girls at the concert.
So, the algebraic expression for the number of boys at the beginning of the concert in terms of p is:
b = (3/10) * p
To solve this problem, we need to use the given information to create an equation and then solve for the number of boys at the beginning of the concert.
Let's denote the number of boys at the beginning of the concert as "b".
According to the given information:
- After 14 boys leave, the ratio of boys to girls becomes 3:10.
- The number of girls at the concert remains the same.
Since the ratio is 3:10, there are 3 boys for every 10 girls.
Now, let's express the number of boys after 14 leave in terms of "b":
Number of boys after 14 leave = b - 14.
Since the ratio of boys to girls is 3:10, we can create the following equation:
(b - 14) / p = 3/10
To solve for "b", we can cross multiply:
10(b - 14) = 3p
Expanding the equation:
10b - 140 = 3p
Isolating "b" by adding 140 to both sides:
10b = 3p + 140
Dividing both sides by 10:
b = (3p + 140) / 10
Therefore, the algebraic expression for the number of boys at the beginning of the concert in terms of p is:
b = (3p + 140) / 10