Rainbow Harbor Cruises charges $16/adult and $8/child for a round-trip ticket. The records show that, on a certain weekend, 900 took the cruise on Saturday and 600 took the cruise on Sunday. The total receipts for Saturday were $12,800, and the total receipts for Sunday were $7,200. Determine how many adults and children took the cruise on Saturday and on Sunday.
900=A+C
12,800=16A+8C
those are the saturday equations. For Sunday, change the second equation to 7200=..
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Let's assume that the number of adults who took the cruise on Saturday is 'x', and the number of children is 'y'.
Therefore, we can write the following equations based on the given information:
1) x + y = 900
2) 16x + 8y = 12,800
Similarly, let's assume that the number of adults who took the cruise on Sunday is 'a', and the number of children is 'b'.
Therefore, we can write the following equations based on the given information:
3) a + b = 600
4) 16a + 8b = 7,200
We will solve these equations to find the values of 'x', 'y', 'a', and 'b'.
To determine the number of adults and children who took the cruise on Saturday and Sunday, we can set up a system of equations.
Let's suppose the number of adults who took the cruise on Saturday is A1 and the number of children is C1.
Similarly, let's suppose the number of adults who took the cruise on Sunday is A2 and the number of children is C2.
From the given information, we can write the following equations:
Equation 1: A1 + C1 = 900 (Total number of passengers on Saturday)
Equation 2: A2 + C2 = 600 (Total number of passengers on Sunday)
We also know the ticket prices, so we can calculate the total revenue for each day:
Equation 3: 16A1 + 8C1 = 12800 (Total revenue on Saturday)
Equation 4: 16A2 + 8C2 = 7200 (Total revenue on Sunday)
We now have a system of four equations with four unknowns. To solve it, we will use the substitution method.
From Equation 1, we can express A1 in terms of C1: A1 = 900 - C1
Similarly, from Equation 2, we can express A2 in terms of C2: A2 = 600 - C2
Now, substitute these expressions for A1 and A2 into Equations 3 and 4:
16(900 - C1) + 8C1 = 12800 (Substitute A1 into Equation 3)
16(600 - C2) + 8C2 = 7200 (Substitute A2 into Equation 4)
Simplifying these equations, we get:
14400 - 16C1 + 8C1 = 12800 (Expand Equation 3)
9600 - 16C2 + 8C2 = 7200 (Expand Equation 4)
Combining like terms, we have:
-8C1 = -1600 (Combine terms on the left side of Equation 3)
-8C2 = -2400 (Combine terms on the left side of Equation 4)
Dividing both sides of these equations by -8, we get:
C1 = 200 (Number of children on Saturday)
C2 = 300 (Number of children on Sunday)
Now, substitute these values of C1 and C2 back into Equations 1 and 2 to find A1 and A2:
A1 = 900 - C1 = 900 - 200 = 700 (Number of adults on Saturday)
A2 = 600 - C2 = 600 - 300 = 300 (Number of adults on Sunday)
Therefore, on Saturday, 700 adults and 200 children took the cruise. On Sunday, 300 adults and 300 children took the cruise.