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A pharmacist has 40%0 and 80% iodine solutions on hand: How many liters of each iodine solution will be required t0 produce 6 liters of 50% iodine mixture?...

Question

A pharmacist has 40%0 and 80% iodine solutions on hand: How many liters of each iodine solution will be required t0 produce 6 liters of 50% iodine mixture?

A pharmacist has 40%0 and 80% iodine solutions on hand: How many liters of each iodine solution will be required t0 produce 6 liters of 50% iodine mixture?



Answers

Chemistry A chemist has one solution that is $80 \%$ acid and a second solution that is $30 \%$ acid. How many liters of each solution will the chemist need in order to make $50 \mathrm{L}$ of a solution that is $62 \%$ acid?

In this question, we're being asked to find how many leaders of 25% acid solution must be added to 80 leaders of 40% acid solution to produce a solution that is 30% acid in the question. They gave us some information, and we can start by talking about the 25% acid solution. That's the one we have to find. So that's gonna be our variable. So we're gonna save point 25 times x X being the number of leaders that we don't know yet, plus 40% 400.40 times the et leaders that were adding it to has to add up to the total number of leaders were going to have that will have a 30% um, acid solution. So we're gonna do 0.30 times ex being that number of leaders and the 80 leaders, and we're going to use our algebra skills to solve this equation. The first thing we want to do is simplify both sides. I'm going to start with the left. I'm not going to do anything to the 0.25 x, so I'm just going to bring it down to my next line 0.40 times 80 is 32. So we're gonna multiply that out and get 32. We're going to distribute this 30% to both parts of what's inside the parentheses. So point 30 X plus and 30% of 80 is 24. Now, we're going to move all variables to the same side. And since I have a smaller quantity here than here, I'm going to go ahead and move it to the right. So I'm gonna subtract 0.25 x Trumble sites and I'm gonna bring down. My 32 equals 30 minus 25 is five. So this will be 50.5 X plus 24. Now, I will move all of my numbers to the other side of the equation so that I can isolate fix. Going to subtract 24 from both sides 30 to minus 24 is eight. And what I have left over here is 0.5 x. This is multiplication toe undo multiplication. To isolate the X, we're going to divide by 0.5 on both sides so that we keep it equal and we find that X is equal to 160. Now our question originally was talking about leaders. So what we know is that we will need to add we'll add 160 leaders. Oh, 25 percent acid solution.

Here's an interesting problem where we are mixing two solutions together where one has 50% concentration and the other has 8% concentration. And together we want a certain percentage concentration of 100 total milliliters. So what this looks like is some number of milliliters of the first solution, plus another number of the second solution enough equaling 100 total milliliters. And then also we want the specific percentages to be relevant. So we're basically saying this 50% of the X solution plus 80% of the UAE solution we wanted to total 68% of the 100 milliliter solution. And this just becomes a system of equations that we just have to work with personages or decimals here and solve for how much of each solution we need. So I'm gonna rewrite this second equation with decimals, and so this would be 0.5 x plus point eat. Why? When 68% is 680.68 times 100 is 68. Now, I can replace either my ex or my Y by solving for that respective variable in this first equation. So what I could do is maybe replace this X with 0.5. Not X would be subtracting away from both sides of this equation, which would just give me 100 minus fly, plus the remainder of that equation, and go ahead and distribute here. So 0.5 times 100 is 50 minus 0.5. Why plus 0.8 y people 68 and then start combining your lifetimes and sold for a while. Second, subtract 50 from both sides. I couldn't simultaneously combined these like terms here, so 50 cancers up negative 500.5 y plus 0.8 wide is a 0.3 wire in 68. Minus 50 gives me 18. Go ahead and divide by that coefficient to get wide by itself. And I get why equals 60 again. This is the quantity of our wide concentration. Are why solution? It's unit here is milliliters, and I know that the combination of X and Y is going to combine to 100 milliliters. Second, simply substitute and do this attraction to determine that the X solution is going to be 40 millimeters and then you complain goes like an to double check that it works for both equations. We know that 40 and 60 equals 100 Then you could multiply by the percentages and see if it also because that 68% as well.

For this problem, we need to figure out how many leaders of a 5% solution must be added to 20 leaders of a 10% solution to end up with an 8% solution are known quantity right now is that we have 20 leaders of 10% solution. So we're gonna say 10% times 20 leaders, and then we know that we're going to have a 5% solution. So that's 50.5 and we don't know how many leaders. So we're gonna call that X. And we know that when we add these two together, we're going to end up with a total mixture of 8% 80.8 of the combined amount of solutions. So 20 plus X, first thing we're going to do is simplified both sides of the equation. Ah, 10% of 20 is too, plus 0.5 x 8% of 20 is one going to six plus 0.8 necks. The first step I want to do is move all of my variables toe one side of the equation. Since 0.5 is less than 0.8 I'm going to move it to the other side through subtraction. It's on this attract 0.5 from both sides and I'm left with two on the left hand side equals 1.6 plus 0.3 x. Now I need to isolate X by using inverse operations and the subtract 1.6 from both sides. Tu minus 1.6 is point for and that is equal 2.3 x. I am going to divide both sides by 0.3 so that I have X by itself 0.4 divided by 0.3 when entered on your calculator will give you 13.3 repeating, which is the same as 13 and 1/3. So 13 and 1/3 is X X was our number of leaders. So we need to add, so add 13 and 1/3 leaders of five percent solution.

Yeah. Let X be dough. 25% antifreeze solution Mix to it for literature. 60%. And the resolution. Okay, to get a mixture that is 45% anti church. This is the information given. So here. Amount of 25%. And if it solution is you do You're a point 25 25 personal 0.25 into Thanks. No, see, this is given amount of 60% interface. Solution is this is here for later given question in question. It is given us. This is for later. Yeah. So zero point six into for you to this is a little bit in the question. And make sure you each 1st 2028% of X. This is the accent, is it poor leader? So I express. Well, you just no contraindications. This is given image. 0.25 eggs. Close your a 0.6 and two four. They worried about explodes for condo Europe work. What faith? No. Tell me Europe weren't. This is 45 minutes, 45%. So every 10 minutes 0.45 now 0.25 Next. This is part 16 to 42.4 one for a giggle to here. Do you have one for five weeks? Flaws. You have 145 indoor. Paul, We wanted to get it yet. No, you don't. Born full five X minus zero point four or five years. Did you go to this is 1.8. So 1.8 minus two point four no minus due to a point two X is equal. Go minus zero point six. What? Minus? Minus cancer. And here X is equal to 16 May. When to Not to each. Excuse me. Three up. Absolutely. This is the answer. So here to tell you that off 25% and official Lucien mix to it. Pull it off. 60% solution to make mixture of for 3% of the fridge. The sea dancer. Yeah.


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