Find the amount of lemonade that needs to be combined to get the answer

Question

Lemonade is available in only two types with different lemon juice concentrations:

Type 1 is made by mixing one jug full of lemon juice with two jugs full of water.

Type 2 is made by mixing one jug full of lemon juice with five jugs full of water.

A customer wants to alter the concentration of lemonade so that it has the same concentration as if it had been made by mixing an amount of lemon juice with three times that amount of water.

Find the amount of type 1 lemonade and the amount of type 2 lemonade that should be combined to make 400ml of lemonade

Answer 1

Note concentration of lemon juice = (volume of lemon juice)/(Total volume of lemon juice and wate)

Concentration of lemon juice in 1st mix: c1 = 1/(1+2) = 1/3

Concentration of lemon juice in 2nd mix :c2 = 1/(1+5) = 1/6

Required concentration: 1/ ( 1+3) = 1/4. AMount of lemon juice with this concentration in 400ml mix = (1/4)(400) = 100 ml

Let amount of Mix-I needed is A ml. Amount of Mix-II needed is 400 - A ml

Total amount of lemon juice in the new mix = c1(A) + c2(400-A) = A/3 +400/6 -A/6 = 200/3+A/6

So 200/3 +A/6 = 100

-200/3 -200/3

A/6 = 100/3

A = 200.

200 ml of mix-I and 200ml of mix-II should be combined.

Cross check: [200(1/3) + 200(1/6)]/ 400 = (300/3)/400 = 1/4 = required concentration.