mix 20% juice with 50% juice to get 40% juice and 200 litres, what is the litres of juice in 20% and 50%

Question

at an occasion of a family gathering, two containers of lemon juice are available, one of the containers is 20% sugar,too sour and the second is 50% sugar too sweet, 200 litres are needed for the family gathering and a 40% sigar mix is considered just right, find how much juice to take from each of the two containers

Answer 1

The idea is to have x liters of 0.2 concentration and (200 - x) liters of 0.5 concentration to produce 200 liters of 0.4 concentration. (200 - x avoids introducing a y.)

0.2x + 0.5(200-x) = 0.4(200)

0.2x + 100 - 0.5x = 80

-0.3x = -20   or 0.3x=20

x = 66.66..... liters of 20% concentration

200-x = 133.33..... liters of 50% concentration

Answer 2

Let x = liters of 0.2 concentration

(200 - x) liters of 0.5 concentration to get 200 liters of 0.4 concentration.

By given data we have
0.2x + 0.5(200-x) = 0.4(200)
0.2x + 100 - 0.5x = 80
-0.3x = -20
or 0.3x=20

Hence 66.66 liters of 20% concentration and 133.33 liters of 50% concentration

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