Final answer:
Using algebra, we determine that the number of boys at the country concert is 44 by setting up a ratio equation and using the information that there are 66 more girls than boys.
Step-by-step explanation:
To solve the problem concerning the ratio of boys to girls at a country concert, we are given that the ratio of the number of boys to the number of girls is 2:5. Additionally, it's stated that there are 66 more girls than boys present. To find out how many boys are at the concert, we'll use algebra.
Let's introduce variables to represent the number of boys and girls:
- Let b be the number of boys.
- Let g be the number of girls.
The ratio given can be expressed as:
b/g = 2/5
From the information about the difference in their numbers, we also have:
g = b + 66
Now, we substitute g from the second equation into the first:
b/(b + 66) = 2/5
Multiplying both sides by 5(b + 66) to get rid of the fraction, we get:
5b = 2(b + 66)
Distribute the 2 on the right side of the equation:
5b = 2b + 132
Subtract 2b from both sides to isolate b:
3b = 132
Divide both sides by 3:
b = 44
Therefore, there are 44 boys at the concert.