Rainbow Harbor Cruises charges $16/adult and $8/child for a round-trip ticket. The records show that, on a certain weekend, 1400 took the cruise on Saturday and 1000 took the cruise on Sunday. The total receipts for Saturday were $18,400, and the total receipts for Sunday were $12,000. Determine how many adults and children took the cruise on Saturday and on Sunday
thanks for helping ms sue
To determine the number of adults and children who took the cruise on Saturday and on Sunday, we can set up a system of equations based on the given information.
Let's assume that the number of adults who took the cruise on Saturday is "A" and the number of children who took the cruise on Saturday is "C".
We know that the total number of people who took the cruise on Saturday is 1400, so the equation is:
A + C = 1400 Equation 1
The total receipts for Saturday were $18,400, and since each adult pays $16 and each child pays $8, we can set up the equation for the total amount of money collected on Saturday:
16A + 8C = 18,400 Equation 2
Similarly, let's assume that the number of adults who took the cruise on Sunday is "B" and the number of children who took the cruise on Sunday is "D".
We know that the total number of people who took the cruise on Sunday is 1000, so the equation is:
B + D = 1000 Equation 3
The total receipts for Sunday were $12,000, so the equation for the total amount of money collected on Sunday is:
16B + 8D = 12,000 Equation 4
We now have a system of four equations. Let's solve them to find the values of A, B, C, and D.
From Equation 1, we can solve for A:
A = 1400 - C
Substituting this value into Equation 2, we can find the value of C:
16(1400 - C) + 8C = 18,400
22,400 - 16C + 8C = 18,400
-8C = -4,000
C = 500
Now that we have the value of C, we can substitute it back into Equation 1 to find A:
A = 1400 - 500
A = 900
Similarly, we can solve Equations 3 and 4 to find the values of B and D.
From Equation 3:
B = 1000 - D
Substituting this value into Equation 4:
16(1000 - D) + 8D = 12,000
16,000 - 16D + 8D = 12,000
-8D = -4,000
D = 500
Substituting the value of D back into Equation 3:
B = 1000 - 500
B = 500
So, on Saturday, 900 adults and 500 children took the cruise, and on Sunday, 500 adults and 500 children took the cruise.