Jane's Orange-Pineapple Drink (2) 11) On the following day, Jane had made 64 ounces of her orange- pineapple drink, which is 25% pineapple juice. After having given 12 ounces of it to her son, who wasn't overly fond of pineapple juice, Jane thought she'd lessen the pineapple juice to just 15%. To do so, how many ounces of orange juice will she have to add? Here are two different ways we can solve this: 0.75(52) + 1.00(x) = 0.85(52 + x) As you can see in this formula, we are focusing on changing the 75% of orange juice to 85%. Change the decimal numbers to whole numbers by multiplying by 100: 75(52) + 100(x) = 85(52 + x) x = ounces of orange juice The first term multiplies the 52 ounces by 75 (from the percent of orange juice). The second term adds 100 times the number of ounces (x) of the pure orange juice. Since it is pure orange juice, it is 100%. The term to the right of the equal sign is the result we want to obtain: a drink with 85% orange juice, which will be the previous 52 ounces, plus the additional ounces of orange juice added to it; and which will, thus, reduce the amount of pineapple juice to 15%.. Now let us work out this problem: 75(52) + 100(x) = 85(52 + x) 3,900 + 100x = 4,420 + 85x 100x = 520 + 85x 15x = 520 x = 34.66 (ounces) Let's double-check this: Before: After (new mixture) 52 ounces 86.66 ounces (52 + 34.66) 75% orange juice 85% orange juice 25% pineapple juice 15% pineapple juice 39 ounces of orange juice 73.661 ounces of orange juice 13 ounces of pineapple juice 12.999 ounces of pineapple juice ------------------------------ --------------------------------- 52 total ounces 86.660 total ounces Here's another way we can do it: If we had a 52-ounce mixture of cleaning fluid and water, which was 25% cleaning fluid, but wanted to dilute the cleaning fluid to 15%, we would just add the right amount of water to it. When we make a reduction in this way, using water, we use 0% to signify the water, as in the following example, which we will also use for our orange-pineapple drink solution: 0.25(52) + 0.0(x) = 0.15(52 + x) Change the decimal numbers to whole numbers by multiplying by 100: 25(52) + 0(x) = 15(52 + x) x = ounces of orange juice The first term multitplies 52 ounces with 25 (the percent of the pineapple juice). In looking at this above formula, it seeks to solve "x," which is representing the ounces of orange juice that are needed to make it a true equation. "How many ounces of orange juice must I add to the 52-ounce mixture of orange juice and pineapple juice in order to reduce the 25% of pineapple juice to 15%?" 25(52) + 0(x) = 15(52 + x) 1300 = 780 + 15x 520 = 15x x = 34.66 (ounces of orange juice)