Solve each problem. See Example 3. How much water should be added...

Question

Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?

Accepted Answer

Hey, everyone in this problem, pure water is added to 42 ml of 13% lime solution. We're asked to find out the volume of water required to decrease the concentration to 7%. We're given four answer choices. option a 36 ml Option B 42 ml Option C 49 ml and option D ml. So we're talking about the concentration of wine. OK. How do we calculate the concentration and well the concentration a Hawaiian is going to be equal to the volume of the line divided by the total volume. OK. So the concentration is looking at how much of that total volume is made up of wine. Now, what's our current volume of wine and the volume of line that we have, it's gonna be equal to the concentration multiplied by the total volume. Yeah, just rearranging the equation we've written and we're talking about the initial volume of life. The initial concentration we're given is 13%. So 0. Multiplied by the total volume. And that initial volume we have is 42 ml. So the volume of the line that we have is 5.46 ml. All right. Now we're adding water to our concentration. OK. In order to decrease that concentration. So we're not changing the volume of the line, OK? We're not adding any lime, we're not removing any lime. So the volume of lime stays the same. So now we want our concentration and we're going back to that original equation. Let me write it again. The concentration is equal to the volume of lime divided by the total volume. We want our concentration to be 7%, which we can write as a decimal 0.07. We know that the volume of line we have is 5. ml And the total volume. Well, we have the original volume of 42 ml plus we're gonna call it the subscript W, the volume of water that we add. OK. And that V W is what we're looking for. So we can multiply Both sides by 42 ml plus VW. We get 0.07, Multiplied by 42 ml plus VW Is equal to 5.4, 6 ml We're trying to solve for VW. So let's divide both sides by 0.07. We get that 42 ml plus VW Is equal to 78 ml. And we sub can subtract 42 ml to get that. The volume of water that we need to add is 36 ml. All right. So we used the initial concentration, we had to figure out the volume of line in our mixture. And then we used the concentration we wanted to achieve with the volume of lime. We knew we had to figure out what volume of water we needed to add. And we found that the volume of water we needed to add was ml which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

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Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?