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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

The Marquise de Brinvilliers has a blue vial with 340 mL of poison and a green vial containing 0.08 L of the same poison. She wants to obtain a ratio of 1:5 between the contents of the two vials. What volume of poison does she have to transfer and from which vial to which vial?

(historical character from Alexandre Dumas - "Marquise the Brinvilliers" or Hugh Stokes "Madame de Brinvilliers and Her Times 1630-1676")

We must first convert the volumes of poison to the same units:

equation

Assume the quantity is moved from the blue vial to the green vial. Denote the quantity with x.

The amount left in the blue vial is:

equation

The amount in the green vial is:

equation

The amounts must be in a ratio of 1:5:

equation

Apply the property of proportions:

equation

and solve for x.

equation

equation

She has to pour 10 mL from the green vial to the blue vial.