Answer:
To solve this problem, we will use the following steps:
Step 1: Let's assume that the number of adult tickets sold is x and the number of senior/child tickets sold is y
Step 2: We know that the number of senior/child tickets sold was 27 less than twice the number of adult tickets sold, so we can write the equation: y = 2x - 27
Step 3: We also know that the total value of tickets sold was $2,647.50. Since adult tickets sold for $10 each and senior/child tickets sold for $7.50 each, we can write the equation: 10x + 7.5y = 2,647.50
Step 4: Now we have two equations with two unknowns, we can substitute one equation into another to find the value of x and y.
y = 2x - 27
10x + 7.5(2x - 27) = 2,647.50
10x + 15x - 405 = 2,647.50
25x = 3,052.50
x = 122
Step 5: We can substitute the value of x in one of the equation, to find the value of y
y = 2(122) - 27
y = 245
Final Answer: 122 adult tickets and 245 senior/child tickets were sold.
Note: We can check our solution by multiplying the number of adult tickets by $10 and the number of senior/child tickets by $7.5 to check if the total money is $2,647.50 which is true.