A popular fruit drink is made by mixing fruit juices. Such a mixture with 50% juice is to be mixed with another mixture that is 30% juice to get 200 liters of a mixture that is 45% juice. How much of each should be used?

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The final product required is 200 liters of a fruit drink with 45% juice. This is equivalent to 200*0.45 = 90 liters of juice.

The first drink that is being added has 50% juice in it and the second has 30% juice in it. Let the volume of the first drink required be V. As the total final volume is 200, the volume of the second drink is 200 - V.

The amount of juice we have from the two is 0.5*V + 0.3*(200 - V). As this should be equal to 90, we get:

0.5*V + 0.3*(200 - V) = 90

=> 0.5*V + 60 - 0.3*V = 90

=> 0.2*V = 30

=> V = 150

150 liters of the first drink and 50 liters of the second should be used.

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