Question

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

Answer 1

Using the inverse of a Matrix:

Let ‘a’ be adults and ‘c’ 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.

Answer 2

56