Final answer:
To find the number of children in the group, set up a system of equations using the total number of people and the total cost of tickets. Solve the equations to find the values of c and a, representing the number of children and adult tickets. Substitute the value of a back into the equation to find the value of c. In this case, there were 21 children in the group.
Step-by-step explanation:
To find out how many children were in the group, we need to set up a system of equations. Let's represent the number of children's tickets as c and the number of adult tickets as a. We can set up the following equations:
c + a = 35 (since the total number of people is 35)
6.5c + 8.75a = 259 (since the total cost of tickets is $259)
From the first equation, we can solve for c in terms of a: c = 35 - a. Substituting this into the second equation, we have:
6.5(35 - a) + 8.75a = 259
227.5 - 6.5a + 8.75a = 259
2.25a = 31.5
a = 31.5 / 2.25 = 14
Substituting the value of a back into the first equation, we can find c: c + 14 = 35, c = 21
Therefore, there were 21 children in this group.