SOLUTION: Jan wants to make 15L of a 14% sugar solution by mixing together a 20% sugar solution and a 10% sugar solution. How much of each solution must she use?
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Question 1118639: Jan wants to make 15L of a 14% sugar solution by mixing together a 20% sugar solution and a 10% sugar solution. How much of each solution must she use? Answer by ikleyn(52781) (Show Source):
Notice that in this problem all concentrations are in kilograms of the sugar per liter.
Let x be the volume of the 20% sugar solution to mix (in liters).
Then the volume of the 10% sugar solution is (15-L).
The balance equation for the sugar mixture is
0.2x + 0.1*(15-x) = 0.14*15
Simplify and solve for x:
0.2x + 0.1*15 - 0.1x = 0.14*15
0.1x = 0.14*15 - 0.1*15
0.1x = 0.04*15 ====> x = = 0.4*15 = 6.
Answer. 6 liters of the 20% solution should be mixed with 15-6 = 9 liters of the 10% solution.
Check. 0.2*6 + 0.1*9 = 2.1 (kilograms is the total mass of the sugar in two input solutions)
0.14*15 = 2.1 (kilograms is the mass of the sugar in the final mixtures)
The two values coincide, which means that the solution and the answer are correc !
Solved.
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It is a standard and typical mixture problem.
You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.
Read them and become an expert in solution mixture word problems.
