Identifying proportional relationships
- [Instructor] We're told that Mael mixes 15 milliliters of bleach with 3.75 liters of water to make a sanitizing solution for a daycare. The amounts of bleach and water always have to be proportional when he makes the sanitizing solution. Which of the following could be combinations of volumes of bleach and water for Mael's sanitizing solution? And they gave us, actually they gave us five potential combinations, they say pick three. So I encourage you to pause this video and try to figure it out. Remember, he mixes 15 milliliters of bleach for every 3.75 liters of water. Alright, now let's try to work this together. So I'm gonna make a table here. So let's say this is bleach, bleach in milliliters. And lets say this is water in liters. And they tell us that he mixes 15 milliliters, the unit here is milliliters, for every 15 milliliters of bleach for every 3.75 liters of water. So what is the proportionality constant here? If you said the water is equal to some constant times the bleach, well what's going on? Well let's see, what would he have to multiply by? He would have to multiply by 3.75 over 15. Now what is 3.75 divided by 15? Let me actually do it right over here, 15 goes into 3.75. Let's see, 15 goes into 37 two times, we have our little decimal right over here, two times 15 is 30, subtract seven, bring down the five and then 15 times five is 75, five times 15 is 75, it all works out. So we see to go from bleach to water we're multiplying by a proportionality constant of 0.25. So we have to see which of these have the same exact proportionality constant going from bleach to water. So let's see, this next one is 12 and three. So if we multiply 12 by 0.25, do we get three? Yeah, three is one fourth of 12, 0.25, 25 hundredths is the same thing as one fourth so this one checks out. What about going from six to 1.5? Are we multiplying by 0.25? Yeah, 1.5 is one fourth of six or another way to think about it is what is six times 25? It is a 150 so six times 25 hundredths would be a 150 hundredths which is the same thing as 1.5. So this one works. What about three and 0.75? So three and 0.75. Am I multiplying by 0.25? Yeah, if I multiply three times 25 hundredths, I get 75 hundredths so that works. So actually the first three choices are our three answers but let's just verify that the next two are not good answers. So let's see, if I go from 20 to 5.5, and so am I multiplying by 0.25? No, 0.25 which is the same thing as one fourth, one fourth times 20 is five, not 5.5. So that doesn't work. And then going from 11 to 3.75, well we definitely know that's not gonna work because notice we have the same amount of water but we have less bleach. Or you could say what's one fourth of 11? Well that's going to be less than 3.75 so we can rule both of these choices out.