The Manhattan Island cruise Company sold 57 tickets for its Circle-the -Island Cruise. Each adult had to pay $22 for the cruise and each child had to pay $10. If the company's total receipts were $774. How many children went on the cruise?
x+y=57
22x+10y=774
-10(x+y=57
-10x-10y=-570
22x+10y=774
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12x=204
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12 12
x=17
57-17= 40
40 children went on the cruise?
To solve this problem, let's assume the number of adults who went on the cruise is 'A' and the number of children is 'C'.
Given that the company sold a total of 57 tickets, we can write the equation:
A + C = 57 ---(1)
We also know that each adult had to pay $22 and each child had to pay $10. So, the total receipts of the cruise can be expressed as:
Total Receipts = (Number of Adults * Price per Adult) + (Number of Children * Price per Child)
Using the given information, we can write another equation for the total receipts:
$774 = (22A) + (10C) ---(2)
Now we have a system of two equations (equation 1 and equation 2) that we can solve simultaneously to find the values of A and C.
To solve the system of equations, we can use a method called substitution or elimination. In this case, let's use substitution:
From equation 1, we can rewrite it as:
A = 57 - C
Substitute this value of A in equation 2:
$774 = (22 * (57 - C)) + (10C)
Now, solve this equation to find the value of C.