To do this, we have to setup equations and then use substitution to get like terms.
c=children, s=students, a=adults
For total cost: 5350 = 5c + 7s + 9a
Total capacity: 750 = c + s + a
Data given: (.5)(c + s) = a
Now, rearranging the data given equation for (c+s) gives us (c+s)= 2a. Using this and substituting into the total capacity equation for (c+s) will allow us to find a: 750 = 2a + a = 3a which gives us a = 750/3 = 250.
Next, we set a = 250 in total cost and data given equation to get the following:
Total Cost: 5350 = 5c + 7s + 2250 which gives 3100 = 5c + 7s
Total Capacity: 750 = c + s + 250 which gives 500 = c + s
Rearranging total capacity to solve for s: s = 500 - c
Plugging that expression for s into total cost gives us: 3100 = 5c + 7(500-c) = 5c - 7c + 3500.
Solving for c gives us 400 = 2c . Total number of children is c = 200.
Total number of students is s = 750 - 200 - 250 = 300.
