Question

You would like to make orange juice for the Queen of Canada but her tastes are very particular. She requires 400mL of orange juice, but it has to be the correct concentration, which is 23% concentrate. You have some 250mL cans of Windsor Delight OJ concentrate, which asks for 3 cans of water to every can of concentrate. You also have 250mL cans of Budget Brit OJ concentrate, which requires 4 cans of water for every can of concentrate. How much Windsor Delight mixture, and how much Budget Brit mixture will go into every 400mL of Her Majesty's Royal

Answer 1

32 ml of Budget Brit OJ concentrate 60 ml of Windsor Delight OJ concentrate Let's look at what you have available. There are two types of concentrate one of them is 1 can of concentrate to 3 cans of water, or 25% concentrate. The other is 1 can of concentrate to 4 cans of water, or 20% concentrate. What you want is a mixture that has 23% concentrate. Assuming you mixed both concentrates in separate containers and then in turn mixed those together in the proper ratio, the equation to express this is 0.20x + 0.25(400-x) = 0.23*400 Solving for x, first distribute the 0.25, and do the multiplications 0.20x + 0.25(400-x) = 0.23*400 0.20x + 100 - 0.25x = 92 Merge terms -0.05x + 100 = 92 Subtract 100 from both sides -0.05x = -8 And divide by -0.05 on both sides x = 160 So you now know that you need 160 ml of the 20% solution and 240 ml of the 25% solution. So you can now work backwards to determine how much of each concentrate you need. 0.20 * 160 = 32 ml of Budget Brit OJ concentrate 0.25 * 240 = 60 ml of Windsor Delight OJ concentrate