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on problem 91 91 by what percent did the median household so median is middle by what percent did the median household income in country Y decrease from 1970 to 1980 so they want a percentage in 1970 to 1980 median household income alright statement number one tells us in 1970 the median household income in country Y was two-thirds of the median household income in country X so let's write Y in 1970 let's just write 70 because the 19 is redundant the median income in country Y in 1970 is equal to two-thirds of the median income if country X in 1970 that's what statement l1 tells us but one again that doesn't I mean we don't know about what happened in 1980 in country Y so we still can't answer the question statement number two in 1980 the median the median household income in country Y so Y in 1980 was one-half the median household income in country X in 1980 now you might be tempted to say oh to linear equations and two unknowns maybe I can solve for it etc but no there's actually two linear equations in four unknowns right this is y in 1970 is different than Y in 1980 and X in 1970 is different than X in 1980 so there's actually four variables but you say oh no no but we don't need to figure out all the variables we just need to figure out the percent decline right they just say by what percent did the median household income in country Y decrease from 1970 to 1980 so essentially if we could figure out this if we could figure out if we could figure out why 80 over y 71 what the percent decline was right if this number is 0.8 then it would be a 40% decline if this number was 0.5 then would be a 50% decline so whatever this number is that that's essentially 1 - that is a percentage - maybe we just have to figure out this but look I can prove you mathematically that we still can't figured out this because why 80 divided by why 70 that's equal to two-thirds X on the side why 80 so why 80 that's 1/2 X in 1980 divided by 2/3 X in 1970 right and then let's see if we could multiply take this three halves up we get let's see 1 divided by 1/3 3 becomes 3 over 2 so it becomes 3/4 X 80 over X 70 so this we're still you know they never told us what the median with a median household income in country X was in any year so we still can't solve this problem so there's not enough information given next problem 92 a certain group of car dealerships agreed to donate X dollars to a Red Cross chapter for each car sold during a 30 day period what was the total amount that was expected to be donated that was expected to be donated so the total amount let's say donation is going to be equal to is going to be equal to X dollars times the number of cars times cars and this is what we need to figure out we need to figure out what the donations are equal to or the expected donations it says a total of 500 cars were expected to be sold so it is essentially telling us that C is equal to 500 we still can't figure out what D is because we don't know how many dollars are are we getting for each car so that is not enough information by itself statement 260 more cars were sold than expected so the total amount actually donated was $28,000 interesting so so essentially it's saying that C Plus so if you had an extra 60 cars than expected right 500 were expected to be sold actually we could just say 500 were expected to be sold 660 more cars were sold than expected so 60 more were sold than expected so this is the actual number that were sold and then that times the amount donated per car is equal to $28,000 well now we do have enough information to figure out well let's think about it we have enough information from this to figure out X right we could say well actually let's let's let me well we definitely have enough information now to figure out X if we use statement number one I just want to be careful to make sure that we can't solve this just with statement number two so we definitely you know if I just said 560 X is equal to $28,000 then you get X is equal to X is equal to 28,000 over 560 so then the amount that was expected to be donated would be 28,000 over 560 that's what X is whatever that number is times the amount that was the number of cars that were expected to be sold times 500 and actually yeah you you have to have statement 1 there because statement 2 60 more cars were sold actually let me think about that so both combined when I use both of the information it definitely works let me see if I can figure it out just using statement 2 alone I don't think I can but I'm I have a nagging feeling that there may be giving more information than I'm so let me say that the car is expected to C so C so this is what statement 2 actually is telling us I assumed the 500 which I shouldn't have done so statement 2 is actually telling when I have 60 more than the car is expected to be sold times X I raised $28,000 right this alone is not on you you don't know what X or C is because at the end of the day at the end of the day you need to know what x times C is x times C is our goal so if you distribute it this out you get X C+ 60 X is equal to $28,000 and you get X C is equal to 28,000 minus 60 X so this is as much information you can glean just from statement number two so that alone is not enough I mean if you could figure out what X is you're done you actually don't need to know the expected number of cars sold you just would know well actually that's true a statement one so you need both of these statements to solve the problem anyway as you can see I haven't done these problems before so sometimes I'm not sure and and sometimes I might even get him wrong problem 93 problem 93 while driving on the expressway did Robin ever exceed the 55 mile an hour speed limit well who knows statement 1 Robin drove a hundred miles she drove 100 miles well that doesn't tell me whether she ever went more than I'm assuming it's a she I guess it's an androgynous sounding name that still doesn't tell me whether she went over a hundred miles to Robin drove for two hours on the expressway so time is equal to two hours so each of these independently give me no information about how fast she went but I can if I use both of them I can figure out her average speed I can say well she went a hundred miles in two hours average speed is equal to 50 miles per hour now the question is did Robin ever exceed the speed limit well I don't know it's completely possible that she just went up to 50 50 miles an hour well in order to in order to you know we don't know how fast her car accelerates she might just gone you know she accelerated really fast got to 55 stayed there or went down a little bit and ended up averaging at 55 she never exceeded it but she could have easily gone 80 miles an hour at some point and then slowed down and taken a break and had a picnic we don't know so this and this by itself is not enough information to figure out if she ever exceeded the speed limit if her average speed was 56 miles per hour then we know that she had to exceed the speed limit because well at you know at we can assume that at some point while she was going at least 56 miles per hour and especially if we can assume that she started at a standstill because then you'd have to go even faster than the average to make up for the time that you're going slower but anyway there's not enough information here to figure it out just knowing that her average speed was 50 next problem 94 in Jefferson school 300 students study French or Spanish or both if a hundred okay this sounds like a diet Venn diagram French or Spanish or both so this is French this is Spanish so this is French this is Spanish and this right here is both in the intersection if a hundred of these students do not study French okay they study French or Spanish or both there's not an option to do neither if a hundred of these students do not study French how many of these students studied both French and Spanish so Spanish so when they tell us that 100 of these students do not study French that tells us that this area let me color it in a suitably suitably garish color that tells us that oh no that's not what I want to do let me that tells us that this area right here is a hundred so essentially the people who are studying Spanish but but not French is a hundred right and they're asking how many of these students study both French and Spanish so they essentially want to know the intersection of French and Spanish that purple area is what the question asks so let's explore the statements statement number one tells us of the 300 students 60 do not study Spanish 60 no Spanish so that's essentially telling us this area this area not not this just this so that tells us how many study French only that's 60 I still doesn't help us to know the intersection statement number two says a total of two 40 of the students study Spanish 240 study Spanish well I think this alone is enough information right because they're telling us that this purple area plus this yellow area is equal to 240 we want to figure out the purple area right so purple plus of the total number of people who study Spanish it's the people who study French and Spanish which is this purple area plus the people who only study Spanish which they gave us in the problem was a hundred and then statement number two says that that is equal to 240 so the people who study French and Spanish has to be the purple area which is 240 minus 100 which is 140 which we don't have to figure out the number we just have to know that 2 gives us enough information by itself to solve the problem and we don't even need problem number we don't even need statement number one and I'm out of time see you the next video