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we're told that Burger barn makes dipping sauce by mixing two spoonfuls of honey with 1/2 spoonful of mustard sandwich town makes dipping sauce by mixing four spoonfuls of honey with one spoonful of mustard which dipping sauce has a stronger mustard flavor so pause this video and see if you can work through that on your own all right now let's think about the ratios of honey to mustard at each of these restaurants so first let's think about the scenario with burger barn so I'll just say B B for short for burger barn so they have two spoonfuls of honey for every 1/2 spoonful of mustard so the ratio of honey to mustard in terms of spoonfuls is two spoonfuls of honey for every 1/2 spoonful of mustard so this is the ratio of honey to mustard let me write this this is honey and this right over here is mustard now let's look at sandwich town so I'll call that s T so sandwich town makes dipping sauce by having four spoonfuls of honey for every one spoonful of mustard so the ratio of honey to mustard is four spoonfuls - one spoonful so once again that is honey and that is mustard now can we make these equivalent ratios or can we compare them somehow well let's see we have one half spoonful of mustard here we have one spoon of mustard here so what if we multiplied both the mustard and the honey spoonfuls by two that still would be an equivalent ratio because we're multiplying by the same amount so if we multiply by two in both situations you have four spoonfuls of honey for every one spoonful of mustard well that's the exact same ratio that we have at sandwich town so it actually turns out that they have the same concentration of mustard they have the same ratio of honey to mustard four spoonfuls of honey for every spoonful of mustard in either situation let's do another example so here we are asked or we are told we are told Patrick's favorite shade of purple paint is made with four ounces of blue paint so I'm interline that in blue four ounces of blue paint for every three ounces of red paint for every three ounces of red paint so the ratio of blue paint to red paint is 4 ounces of blue four ounces of blue for every 3 ounces of red so for 2/3 which of the following paint mixtures will create the same shade of purple alright pause this video and see if you can figure it out on your own so this is 3 ounces of blue paint mixed with 4 ounces of red paint well this is a ratio here of 3 to 4 and even though it's dealing with the same numbers this is a different ratio the order matters this is four ounces of blue for every 3 ounces of red this is saying three ounces of blue for every 4 ounces of red so we can rule this one out eight ounces of blue paint mixed with six ounces of red paint so here this ratio is 8 ounces of blue for every six ounces of red well are these equivalent ratios well the difference or you can go if you multiply by two in either case you will get 2 8 2 6 4 times 2 is 8 3 times 2 is 6 so this is indeed an equivalent ratio so we would select this one alright here they say 6 ounces of blue paint mixed with 8 ounces of red paint so this is once they've swapped the blues and the red relative to this one so this is a ratio of 6 to 8 so let me write this down so this is a ratio 6 ounces of blue paint for every 8 ounces of red paint so just like we ruled out that first one this is dealing with the same numbers but in the different order and the order matters will rule that out 20 ounces of blue paint 20 ounces of blue paint for every 15 ounces of red paint so are these equivalent well let's think about it to go from 4 to 20 you could multiply by 5 and to go from 3 to 15 you could multiply by 5 so we could multiply by the same factor to go from 4 to 3 to 20 to 15 so this is indeed an equivalent ratio 12 ounces of blue paint mixed with 16 ounces of red paint alright so this is a ratio here of 12 ounces of blue for every 16 ounces of red so let's think about this to go from 4 to 12 you would multiply by 3 now if you multiplied 3 by 3 you would have a 9 here not a 16 so this is definitely not an equivalent ratio another way of thinking about it you have in terms of ounces you have more ounces of blue than you have of red for any of the equivalent ratios but here you have more ounces of red than blue so once again another way of realizing that that is not equivalent so only B and D are the equivalent mixtures that will provide the shade same shade of purple to have that same shade you need the same ratio of blue to red