45 points, brainliest for correct answer!

Admission to a zoo costs $10 for adults and $6 for children. A group of 29 people attending the zoo paid a total of $222 in admission fees.

Part a. Write a system of equations to represent the situation. Let a represent the number of adult admissions, and let c represent the number of child admissions.
Part b. Solve the system you wrote in part (a) using the substitution method. Show your work.
Part c. Interpret your solution in the context of the problem.