 b2sonicxh

2021-12-31

How many liters of a 25% alcohol solution and how many liters of a 12% alcohol solution must be mixed to create 13 liters of a 15% alcohol solution? Timothy Wolff

Step 1
Let the number of liters of 25% alcohol solution and 12% alcohol solution required be x and y
According to question,
$x+y=13$ (1)
$0.25x+0.12y=0.15\cdot 13$
$⇒25x+12y=195$ (2)
Step 2
Multiply Eq.(1) with 12
$⇒12x+12y=156$ (3)
Subtract Eq.(3) from (2)
$13x=39$
$⇒x=3$
From Eq.(1)
$x+y=13$
$⇒3+y=13$
$⇒y=10$
To create 13 liters of a 15% alcohol solution we need 3 liters of 25% alcohol solution and 10 liters of 12% alcohol solution Lakisha Archer

$25x+12\left(13-x\right)=15\cdot 13$
$25x+156-12x=195$
$25x-12x=195-156$
$13x=3913$
$x=$ 3 liters 25.00% Alcohol 1
10 liters 12.00% Alcohol 2 karton

Solution A
Concentration = 25%=0.25
Amount =x
Solution B
Concentration = 12%=0.12
Amount = 13-x
Resultant Solution
Concentration = 15%=0.15
Amount = 13 liters
$\left(\text{Concentration of A}\cdot \text{Amount of A}\right)+\left(\text{Concentration of B}\cdot \text{Amount of B}\right)=\left(\text{Concentration of Resultant}\cdot \text{Amount of Resultant}\right)$
0.25x+0.12(13-x)=0.15 * 13
0.25x+1.56-0.12x=1.95
0.25x+1.56-0.12x=1.95
0.13x=1.95-1.56
0.13x=0.39
0.13x/13=0.39/13
x=3
Amount of solution A = x = 3 liters
Amount of solution B = 13-x = 13-3 = 10 liters