A cleaning solution is made from vinegar, lemon juice, and water. The table shows the part of the total solution that is in each element. Solution Components Solution A Solution B Solution C Vinegar 0 point 1 0 point 2 0 point 4 Lemon Juice 0 point 1 5 0 point 2 0 point 1 Water 0 point 7 5 0 point 6 0 point 5 Mr. Allen needs 100 mL of a solution that is 30 percent vinegar, 15 percent lemon juice, and 55 percent water. How much of solution A will Mr. Allen need to make his cleaning solution?
Let A, B, and C be the amounts of the three solutions in mL. Since the total is 100 mL, their amounts add to 100; using the vinegar and lemon-juice percentages gives 0.1A + 0.2B + 0.4C = 30 and 0.15A + 0.2B + 0.1C = 15. Solving these equations gives A = 0, so Mr. Allen needs 0 mL of solution A.
AI-written and checked against the verified answer.