A cafeteria has a 20 liter drink dispenser filled with a 20% juice mixture. They want the drink in that dispenser to be 40% juice. The plan is to allow the volume in the dispenser to draw down with student purchases and at some point refill the dispenser completely with an 70% fruit juice mixture so that the full dispenser will be 40% fruit juice. Determine how far down they should allow the dispenser to get before refilling with the 70% juice.

piopiopioirp

piopiopioirp

Answered question

2022-11-19

A cafeteria has a 20 liter drink dispenser filled with a 20% juice mixture. They want the drink in that dispenser to be 40% juice. The plan is to allow the volume in the dispenser to draw down with student purchases and at some point refill the dispenser completely with an 70% fruit juice mixture so that the full dispenser will be 40% fruit juice. Determine how far down they should allow the dispenser to get before refilling with the 70% juice.

Answer & Explanation

Phiplyrhypelw0

Phiplyrhypelw0

Beginner2022-11-20Added 24 answers

Initial Volume = 20l 20% juice
Let after 'x' l of 20% juice to removed. We are adding 70% juice of 'x' litreo
Total concetration of juice to 40%
Total volume is again 20 l.
\therefor ( 20 x ) has 20% juice
x has 70% juice
mixture has 40% juice
( 20 x ) 20 % + x × 70 % 20 × 100 = 40 ( 20 x 5 + 7 x 10 ) × 5 = 40 40 2 x + 7 x 10 = 8 40 + 5 x = 80 5 x = + 40 x = + 8
It means, after removing 8l of 20% juice.
we should add 70% juice to get 40% juice

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