Solve the problem.
-The Little Town Arts Center charges $25 for adults, $14 for senior citizens, and $10 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,800 for 792 tickets sold. There were 41 more children than adults. How many children attended?
A)215 children
B)299 children
C)268 children
D)309 children

Question

Quizplus · Accepted Answer

The total number of tickets sold was 792. Let's denote the number of adults as A, senior citizens as S, and children as C. We have three equations based on the information provided:1. $A + S + C = 792$ (total tickets)2. $25A + 14S + 10C = 12800$ (total revenue)3. $C = A + 41$ (41 more children than adults)From equation 3, we can express A in terms of C: $A = C - 41$.Substituting $A = C - 41$ into equation 1 gives us $C - 41 + S + C = 792$, which simplifies to $2C + S - 41 = 792$. However, to solve this system of equations directly, we need to manipulate these equations to isolate one variable.Given the complexity of solving this system with the information provided, we can approach the problem by testing the given options for the number of children and checking which one fits the conditions.Option D, 309 children, when tested with the conditions provided, will satisfy the equations when calculated correctly. This involves substituting the value back into the equations and solving for the other variables to ensure the total revenue matches. This is a more straightforward approach for multiple-choice questions when direct calculation might be too cumbersome without additional information or a mistake in the initial setup.

Solve the Problem. -The Little Town Arts Center Charges $25 for Adults, $14