This problem looks a lot like the other straight forward concentration problems we've been doing but there's going to be a quick trick and I’m going to show you when we get there.
Rudy wants to make a 21% sugar solution. He has already poured 1 fluid ounce of fl oz stands for fluid ounce of pure water into a beaker. How many fluid ounces of 28% per sugar solution must he add to this to create the desired mixture?
Okay so kind of visualize in your head what Rudy is doing, he’s sitting at his chemistry station, he is hopping to get a 21% concentration from his mixture and he started with pure water pure water doesn't have any sugar percent right?
So when I’m doing my amount times concentration for this first ingredient, my amount is one but my concentration of sugar is 0% that's why this is weird. There is ingredient 1, one ounce of 0 concentration sugar plus how many so we don't know but its going to be 28% is going to be equal to some mixture amount and the mixture amount he's going to have is his one ounce of water one, full ounce of water plus however much he puts in of his second solution that's his mixture amount times his mixture percent.
We are going to go through one more time because this is a really tricky problem. He starts with one ounce of 0% sugar my percents represent how much sugar there is. That's where students get really confused this isn't 100% it’s 0% sugar. He is adding to that some amount that we are trying to solve of 28 percent to get his mix. His mix amount is the 1 ounce of water plus the x ounces of the solution 2 to get his mixture and he wants the 21%.
Once you have that you guys can do this problem 1 times 0 is 0, so I’m just going to have point 28x on this side of the equals is going to be equal to let's distribute .21 plus .21x you’re on your way. Subtract .21x from both sides and you'll have .07x equals .21. Divide both sides by .07 and you get 3., X equals 3 fluid ounces
Make sure that makes sense before you check and move on so let's see so 3 fluid ounces of pretty strong stuff is being added to one ounce with 0 sugar in it to get 21%, yeah that makes sense this number is going to go down when I add plane water to it.
It’s going to become less strong just like what Rudy has he has a less strong solution than what he started with. So this one was tricky because we had the thing that said pure water pure water means it’s 0% sugar that's tricky. Watch for that when you are doing these kinds of problems, look out for the word ‘pure’.
Experience the 'A-Ha!' moment with the best teachers
whom we hand-picked for you!
M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
“Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
“Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
“You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”