You are asked to develop an energy drink using: concentrated orange juice, water
ID: 1884755 • Letter: Y
Question
You are asked to develop an energy drink using: concentrated orange juice, water and a salt solution. Energy drink is expected to contain 75% water You are asked to develop an energy drink using: concentrated orange juice, water and a salt solution. Energy drink is expected to contain 75% water You are asked to develop an energy drink using: concentrated orange juice, water and a salt solution. Energy drink is expected to contain 75% water 4. You are asked to develop an energy drink using: concentrated orange juice, water and a salt solution. Energy drink is expected to contain 75% water, 15% sugar, and 10% mineral salts. The concentrated orange juice contains: 45% water, 35% sugar and 20% salts; and the salt solution has 5% salt. Determine the amount of each ingredient in the energy drink formulation. Use MATLAB to calculate the amount of ingredients.Explanation / Answer
given
energy drink = concentrated orange juice + water + salt solution
energy drink mass = m
mass of water = 0.75m
mass of sugar = 0.15m
mass of salts = 0.1m
concentrated orange juice mass = m1
mass of water = 0.45m1
mass of sugar = 0.35m1
mass of salts = 0.2m1
mass of salt solution = m2
mass of salt = 0.05m2
mass of water = 0.95m2
mass of concentrated juice = m1
mass of sale solution = m2
mass of water = m3
then
m = m1 + m2 + m3
also
0.75m = 0.45m1 + 0.95m2 + m3
0.15m = 0.35m1
0.1m = 0.2m1 + 0.05m2
solving
m1/m = 0.15/0.35 = 3/7
m2/m = (0.1 - 0.2*3/7)/0.05 = 2/7
m3/m = 0.75 - 0.45*3/7 - 0.95*2/7 = 2/7
hence we need 3/7 concentrated orange juice, 2/7 water, 2/7 salts
to solve using matlab
syms x y z
eqn1 = 0.45*x + 0.95*y + z == 0.75;
eqn2 = 0.35*x == 0.15;
eqn3 = 0.2*x + 0.05*y == 0.1;
[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [x, y, z])
X = linsolve(A,B)
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