Question 185489: Solve Problems Using Linear Systems
10. Amy needs to make 10 L of 42% sulphuric acid solution. In the supply room, she finds bottles of 30% sulphuric acid solution and 60% sulphuric acid solution. What volume of each solution should she mix in order to make the 42% solution?
(Answers are: 6 L of 30% sulphuric acid solution, 4 L of 60% sulphuric acid solution, but i dont know how to solve it?)
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the number of liters of 60% sulphuric acid solution required, then (10-x) is the number of liters of 30% sulphuric acid soltion required.
What you really need to find is the number of liters of acid in the solution, and this can be expressed by, after changing the percentages to their decimal equivalents, the number of liters of acid in the 10 liters of 4.2% solution equals the sum of the number of liters of acid in the x liters of he 60% solution and the number of liters of acid in the (10-x) liters of 30% solution.
10(0.42) = 0.6x+0.3(10-x) Simplify and solve for x.
4.2 = 0.6x+3-0.3x Subtract 3 from both sides.
1.2 = 0.3x Divide both sides by 0.3
4 = x
Amy needs 4 liters of 60% sulphuric acid solution plus (10-4)= 6 liters of 30% sulphuric acid soltion to obtain 10 liters of 4.% sulphuric acid solution.
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