# college Algebra

Use matrix methods to solve the problem.

120,000 gallons of fuel are to be divided between two airlines. Triple A Airways requires three times as much as Unity Air. How much fuel should be allocated to Triple A?
______ gal

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1. ah ha, you did not say you know linear algebra before. In the earlier problem the determinant of your coefficient matrix was zero, no solutions.

a + u = 120,000
a - 3 u = 0

| 1 +1 | 120,000
| 1 -3 | 0

det coef matrix = -3 - 1 = -4

put right column in for a column to solve for a

| 120,000 +1 |
| 0000000 -3 | all divided by -4

-360,000/-4 = 90,000 for Triple A
then of course Unity gets 30,000

lo and behold, they add up to 120,000

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2. thank you

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