In mixture problems, substances with different characteristics are combined, and it is necessary to determine the characteristics of the resulting mixture. The question involves mixing of two substances with different concentrations resulting in a net mixture of definite concentration. The approach to solve such problems is to create a equation of type:
(Amount of first substance) * (Value or Concentration) + (Amount of second substance) * (Value or Concentration) = (Total Amount) * (Value or Concentration)
Example 1: If 6 pounds of nuts that cost $1.20 per pound are mixed with 2 pounds of nuts that cost $1.60 per pound, what is the cost per pound of the mixture?
The total cost of the 8 pounds of nuts is
6($1.20)+2($1.60) = $10.40
The cost per pound is $10.40/8 = $1/30
Example 2: How many liters of a solution that is 15 percent salt must be added to 5 liters of a solution that is 8 percent salt so that the resulting solution is 10 percent salt?
Let n represent the number of liters of the 15% solution. The amount of salt in the 15% solution (0.15n) plus the amount of salt in the 8% solution [(0.08)(5)] must be equal to the amount of salt in the 10% mixture [0.10(n+5)]. Therefore,
0.15n + 0.08(5) = 0.10(n+5)
n = 2
Two liters of the 15% salt solution must be added to the 8% solution to obtain the 10% solution.