Rainbow Harbor Cruises charges $16/adult and $8/child for a round-trip ticket. The records show that, on a certain weekend, 700 took the cruise on Saturday and 600 took the cruise on Sunday. The total receipts for Saturday were $9,600, and the total receipts for Sunday were $7,200. Determine how many adults and children took the cruise on Saturday and on Sunday.
To solve this problem, we can set up a system of equations. Let's assume that the number of adults who took the cruise on Saturday is a and the number of children is c. Similarly, let's assume that the number of adults who took the cruise on Sunday is b and the number of children is d.
From the given information, we can write two equations:
Equation 1: a + c = 700 (total number of passengers on Saturday)
Equation 2: b + d = 600 (total number of passengers on Sunday)
We also know the ticket prices, so we can calculate the total receipts for each day as:
Total receipts on Saturday = 16a + 8c = $9,600
Total receipts on Sunday = 16b + 8d = $7,200
Now, let's solve this system of equations to find the values of a, b, c, and d.
From Equation 1, we can rewrite it as c = 700 - a and substitute it into the equation for total receipts on Saturday:
16a + 8(700 - a) = 9,600
16a + 5,600 - 8a = 9,600
8a = 9,600 - 5,600
8a = 4,000
a = 4,000 / 8
a = 500
Now, substitute the value of a into Equation 1 to find the value of c:
c = 700 - 500
c = 200
Similarly, from Equation 2, we can rewrite it as d = 600 - b and substitute it into the equation for total receipts on Sunday:
16b + 8(600 - b) = 7,200
16b + 4,800 - 8b = 7,200
8b = 7,200 - 4,800
8b = 2,400
b = 2,400 / 8
b = 300
Now, substitute the value of b into Equation 2 to find the value of d:
d = 600 - 300
d = 300
Therefore, the number of adults and children who took the cruise on Saturday is 500 and 200 respectively, while the number of adults and children who took the cruise on Sunday is 300 and 300 respectively.