Ratios and proportions | Worked example

- [Instructor] We're told that Ramon's restaurant, three enchiladas cost the same as five tacos, and seven tacos cost the same as three burritos. Which of the following cost the same? So pause this video and see if you can figure this out, and you'd only pick one of these choices. All right, now let's do it together. And when you tackle a problem, it's dealing with ratios, but my brain makes it, finds it easier to work on this if we have some numbers attached to how much an enchilada costs and how much a taco costs. So, let's see if we can make these numbers work out. So, let's say that an enchilada costs $5. So I'm just making up that number here. So, enchilada, enchilada is $5. And so three enchiladas so three times, I'll say E N C H is gonna be equal to $15. And then if that's the same as five tacos, I'm just looking at this first part over here, three enchiladas cost the same as five tacos, that if an enchilada cost $5, three enchiladas cost $15, well then five tacos cost $15. So five times tacos is equal to $15. In which case, the tacos would be $3. So taco's would be equal to, I'll just say tacos are $3. And then seven tacos would be the same as three burritos. So seven times tacos, that's gonna be equal to $21, that's gonna be the same thing as three burritos. So three times, I'll just say B U R for burritos, is equal to $21 and then divide both sides by three, our burrito is gonna be $7 each. So our burrito is going to be $7. So on this tangible example where an enchilada is $5, but I picked this to make things more tangible, if enchiladas are $5 then tacos are $3 and burritos are $7. And so let's see which of these make sense: So which of the following would cost the same? Would three enchiladas cost the same as three burritos? Well no, three enchiladas are $15 while three burritos as $21. So that's not gonna be the same. And you could have even ruled that out before by saying look three enchiladas cost the same as five tacos, you could write this in terms of tacos, and three burritos cost the same as seven tacos. So that's another reason why those two aren't gonna be the same. So four enchiladas and five burritos. So see four enchiladas are gonna be $20, four times five, five burritos are gonna be $35. So we can rule that one out. Five enchiladas and seven burritos. Alright, five enchiladas, five times five, that's gonna be $25. Seven burritos are gonna be $49. Nope, we can rule that one out. Seven enchiladas and five burritos. This is interesting. Seven enchiladas times five, $35. Five burritos, five times seven, $35. This one looks good. Now let's see if we can just rule this one out as well, nine enchiladas, that's gonna be $45, seven burritos are $49. And so these also are not equal.