Question 21322: Solution A, which is 10% iodine, is mixed with solution B which is 18% iodine, to obtain 320 grams of a solution that is 15% iodine. How many grams of solution A and how many grams of solution B is needed for the 15% iodine solution?
Answer by Kuroinu(8)   (Show Source):
You can put this solution on YOUR website! I'm going to take you through how to solve this problem using two variables, but there is also a way to solve this type of problem with one variable, so keep that in mind if this gets confusing. You first want to set up a table that has Solution A and Solution B. In the first row, you would have Solution A, .1 (or 10%), x (the variable representing the amount of solution A used), and .1x (to represent the over all value of solution A). For the second row, you would do the same for Solution B, having Solution B, then .18, then y, and .18y. Note that this is just to organize your information and that you don't always have to do it. Now you would set up the two equations that will be used to solve this. The first is .1x+.18y=.15(x+y). This equation represents that by adding 10% of the amount of Solution A to 18% of the amount of Solution B, you would get 18% of the amount of both solutions used. The second equation is simply x+y=320, which states the overall amount of both solutions. Now to solve for the amounts of x and y. We will first solve for y because this will be easier to do and will not make you work with negatives. To solve for y, we will replace x in the first equation with 320-y, since that is equal to x, and replace x+y with 320. The new equation will look like .1(320-y)+.18y=.15(320). Distribute the .1 on the first side and the .15 on the second to get 32-.1y+.18y=48. Now simplify this further by combining the like terms of y to get 32+.08y=48. Subtract the 32 to get the y term by itself and get .08y=16, and finally divide both sides by .08 to get that y=200. Now we know how much of Solution B is used. Using this, we can find how much of Solution A is used by putting the y value into the second equation. So now we have that x+200=320. Subtract 200 from both sides and we get x=120. So 120 grams of Solution A and 200 grams of Solution B are used to make the 320 grams of the 15% solution. If you wish to check the answer, you can put the x and y values into the original equation and check to make sure that both sides are equal, which they should be, provided that I didn't make any mistakes. I hope that wasn't too hard to understand, I'm not the best at explaining things, and I hope this helps you if you have futre problems like this.
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