# 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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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.

Let the volume of the mixture with 50% juice that has to be used be l, the volume of the mixture with 30% juice used is 200 - l.

As the final mixture has 45% juice,

50*l + 30*(200 - l) = 45*200

=> 50l + 6000 - 30l = 9000

=> 20l = 3000

=> l = 150

**The volume of the mixture with 50% juice that has to be used is 150 liters and 50 liters of the mixture with 30% juice is used. **

Total Mixuture volume = 200 l

Juice percentage = 45%

Juice Quantity = 200*45/100 = 90 l

Let The quntity of mixture with 50% Juice be x, and that with 30% juice be y

Then

x+y = 200 => y = 200-x

Quantity of juice in two mixtures:

X*50/100 +y*30/100 = 90

5x +3y = 900

Substituting value of y in above we get:

5x + 3*(200-x) = 900

5x + 600 - 3x = 900

2x = 300

x = 15o

y = 200-150 = 50

**150 litres of mixture with 50% juice **is to be used with

**50 litres of mixture with 30% juice **to get

**200 litres with 45% juice**.