At a concert, 80% of the people were adults. 75% of the children at the concert were boys. There were 130 fewer boys than adults.

1. Find the percentage of people who were children

$\text{Percentage of children} = 100\% - 80\% = 20\%$

2. Calculate the percentage of boys among all the people

$\text{Percentage of boys} = 75\% \text{ of } 20\% = \frac{75}{100} \times 20\% = 15\%$

1. Find the percentage of people who are boys and adults to set up the difference.

From the first part of the question:

• Adults = $80\%$
• Children = $100\% - 80\% = 20\%$
• Boys = $75\%$ of Children = $0.75 \times 20\% = 15\%$
• Difference between adults and boys = $80\% - 15\% = 65\%$

2. Calculate the total number of people and the number of adults and children.

Given that there are 130 fewer boys than adults:
$65\% \text{ of total people} = 130$
$1\% \text{ of total people} = \frac{130}{65} = 2$
$\text{Total people} = 200$

Number of adults = $80\% \text{ of } 200 = 160$
Number of children = $20\% \text{ of } 200 = 40$

3. Calculate the cost of an adult ticket using total sales.

Let the cost of an adult ticket be $u$ dollars.
The cost of a child's ticket is $40\%$ of $u = 0.4u$ dollars.

Total revenue gathered:
$\text{Total revenue} = (160 \times u) + (40 \times 0.4u) = 2640$
$160u + 16u = 2640$
$176u = 2640$
$u = \frac{2640}{176} = 15$

Thus, an adult ticket costs $15.