math
posted by nikki on .
rainbow Harbor Cruises charges $16/adult and $8/child for a round trip ticket. The records show that on a certain weekend, 1200 people took the cruise on saturady and 800 people took the cruise on sunday, The total receipte for saturday were $13,600 and the total receipts for sunday were $9,600. Determine how many adults and children took the cruise on saturday and sunday set up two systems o linear equations and use the inverse of the coefficient matrices to answwer the question

Using the inverse of a Matrix:
Let āaā be adults and ācā be children
a + b = 1000
16 a + 8b = 12,800
1 1 1000 16 R1 (R2) 1 1 1000 R2 / 8
16 8 12800 0 8 3200
1 1 1000 1 R2 + R1 1 0 600
0 1 400 0 1 400
Therefore, there were 600 adults and 400 children on Saturday.
SUNDAY
a + b = 800
16a + 8 b = 9600
1 1 1000 16 R1 (R2) 1 1 1000 R2 / 8
16 8 12800 0 8 3200
1 1 1000 1 R2 + R1 1 0 400
0 1 400 0 1 400
Therefore there were 400 adults and 400 children on Saturday. 
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