Marlene is solving a number puzzle involving three rational numbers a, b, and c. here are her clues:
the quotient of a and c is 8.
the product of a and c is 2.
the quotient of a and b is -16.
the product of a and b is -1.
the quotient of b and c is -0.5.

a = 4, b = - 0.25, c = 0.5

8 is the quotient of either a/c or c/a. Additionally, ac = 2. Therefore either a or c must be 0.5, while the other is 4. This is because 4/0.5 = 8; 4 x 0.5 = 2.

-16 is the quotient of either a/b or b/a. At the same time, ab = -1. Due to this a cannot be 0.5, which would make b -8. If b is -8, then -8 x 0.5 does not equal -1. a must be 4. If a is 4, then c is 0.5. Solve for b, and you will find it is -0.25 (4/-0.25) = -16.

As a final proof, do the final step. The quotient of b/c is -0.5. -0.25/0.5 is in fact -0.5.

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