A cleaner is sold in low and high concentrations so that customers can combine amounts from each in order to obtain a desired quantity and concentration. The low concentration is 3% pure cleaner and the high concentration is 18% pure cleaner. How many liters of the low and high concentrations must be combined to obtain 10 liters that is 8% pure cleaner? Choose 1 answer: (A) 6 liters of low and 4 liters of high (B) 6(1)/(3) liters of low and 3(2)/(3) liters of high (C) 6(2)/(3) liters of low and 3(1)/(3) liters of high (D) 7 liters of low and 3 liters of high

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A cleaner is sold in low and high concentrations so that customers can combine amounts from each in order to obtain a desired quantity and concentration. The low concentration is  3% pure cleaner and the high concentration is  18% pure cleaner. How many liters of the low and high concentrations must be combined to obtain 10 liters that is  8% pure cleaner? Choose 1 answer: (A) 6 liters of low and 4 liters of high (B) 6(1)/(3) liters of low and  3(2)/(3) liters of high (C) 6(2)/(3) liters of low and  3(1)/(3) liters of high (D) 7 liters of low and 3 liters of high

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Define Variables: Let x be the amount of low concentration cleaner needed, and y be the amount of high concentration cleaner needed. We know that x + y = 10 because we want to obtain 10 liters in total.Set Up Equations: We also know that the final mixture needs to be 8% pure cleaner. We can set up an equation based on the concentrations: 0.03x (3% of the low concentration) + 0.18y (18% of the high concentration) should equal 0.08 * 10 (8% of the final 10-liter mixture).Solve Using Substitution: Now we have two equations: 1) x + y = 10 2) 0.03x + 0.18y = 0.8 We can solve this system of equations using substitution or elimination. Let's use substitution. From equation 1), we can express y as y = 10 - x.Substitute and Simplify: Substitute y = 10 - x into equation 2): 0.03x + 0.18(10 - x) = 0.8 Now, distribute the 0.18 into the parentheses: 0.03x + 1.8 - 0.18x = 0.8 Combine like terms: -0.15x + 1.8 = 0.8Isolate Variable: Subtract 1.8 from both sides to isolate the term with x: -0.15x = 0.8 - 1.8 -0.15x = -1Find Low Concentration Amount: Divide both sides by -0.15 to solve for x: x = -1 / -0.15 x = 6.666... Since we are looking for a practical solution in terms of liters, we can round this to x = 6(2/3) liters of low concentration cleaner.Find High Concentration Amount: Now we can find y by substituting x back into y = 10 - x: y = 10 - 6(2/3) Convert 6(2/3) to an improper fraction: (6 * 3 + 2)/3 = 20/3 y = 10 - 20/3 y = (30/3) - (20/3) y = 10/3 y = 3(1/3) liters of high concentration cleaner.

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