Q You have two bottles of salty water Bottle A contains salt

Q: You have two bottles of salty water. Bottle A contains salt water at a concentration of 20 grams per liter and Bottle B contains salt water at a concentration of 5 grams of salt per liter. How many liters of each must you pour into a third bottle in order to obtain a mixture that is 30 liters at a concentration of 10 grams per liter?

Teacher\'s Answer: 10 L from Bottle A and 20 L from Bottle B.

Note to answerer: Could you list out the steps and reasonings behind solving this problem? Thank you!

Solution

concentration =number of grams of salt_/volume

Bottle A contains salt water at a concentration of 20 grams per liter and Bottle B contains salt water at a concentration of 5 grams of salt per liter

=>C_A =20 g_/L ,C_B =5 g_/L

let x L from Bottle A and y L from Bottle B are mixed

mixture that is 30 liters at a concentration of 10 grams per liter

total salty water :x+y =30L

total salt:(20x +5y) grams

concentration of mixture:(20x +5y)_/30 =10 g_/L

x+y =30,20x+5y=30*10

=>y=30-x , 20x+5y=300

=>20x +5(30-x)=300

=>20x +150-5x=300

=>15x=150

=>x=10

x+y=30, x=10

=>10+y=30

=>y=20

so 10 L from Bottle A and 20 L from Bottle B are to be mixed   to obtain a mixture that is 30 liters at a concentration of 10 grams per liter