## Milo wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice mixture that is

Question

Milo wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture

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2 months 2021-09-28T16:06:15+00:00 2 Answers 0 views 0

1.5gal

Step-by-step explanation:

From the given information:

50% lemon juice + 50% lime juice is the intended mixture.

Therefore, to find quantity that would be added to 20% lemon juice and 80% lime juice, let’s assume this to be x.

x of 100% and 4-x gallons of the existing 20% mix

100%x + 20%(4-x) = 50%(4)

1.00x + 0.2(4-x) = 0.5(4)

1.00x + 0.8-0.2x = 2

1.00x-0.2x = 2-0.8

0.8x = 1.2

× = 1.5gal.

The answer to the question is;

1.5 gallons of 100% lemon juice added to 2.5 gallons of 20% lemon juice + 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture.

1.5 gallons of 100% lemon juice

Step-by-step explanation:

To solve the question, we note

Desired concentration = 50% lemon juice and 50% lime juice

Available concentration = 100% lemon juice and 20% lemon juice and 80% lime juice

To make  4 gallons of 50% lemon juice and 50% lime juice Milo requires

20 per 100 lemon requires 60 parts of pure lemon to make 160 parts of 50% lemon juice and 50% lime juice

100 requires 60 to make 160

100/160 requires 60/160 to make one part of 50% lemon juice and 50% lime juice

That is 5/8 gallon of 20 % lemon requires 3/8 gallon of pure lemon to make 1 gallon of 50% lemon juice and 50% lime juice

That is 2.5 gallons of 20 % lemon requires 1.5 gallons of pure lemon to make 4 gallons of 50% lemon juice and 50% lime juice

Milo should add 1.5 gallons of 100% lemon juice to 2.5 gallons of a juice mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture