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Manuel wants 30 liters of a mixture of water and 10% lemon juice. He has a mixture of 8% lemon juice and a mixture of 20% lemon juice. How many liters of the 8% and 20% mixtures should he mix to get what he wants?

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Raphealnwobiidn

Manuel needs 20 liters of the 8% and 5 liters of 20% mixtures to be mixed so as to get 30 liters of a mixture of water and 10% lemon juice.

Let x represent the amount of 8% lemon juice in liters and y represent the amount of 20% lemon juice in liters.

Since Manuel wants to produce a 30 liters mixture from 8% lemon juice and 20% lemon juice, hence:

x + y = 30      (1)

Also, Manuel wants 30 liters of a mixture of water and 10% lemon juice, hence:

8% of x + 20% of y = 10% of 30 liters

0.08x + 0.2y = 3         (2)

Solving equation 1 and 2 simultaneously; multiply equation 1 by 0.2 and subtract equation 2 from the result:

0.12x = 3

x = 25 liters

x + y = 30

25 + y = 30

y = 5 liters

Manuel needs 20 liters of the 8% and 5 liters of 20% mixture

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