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Current time:0:00Total duration:12:05

We're on problem 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. All right. Statement number one tells us in
1970, the median household income in country Y was 2/3
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 2/3 of the median income of country
X in 1970. That's what statement
one tells us. But one again, we know nothing
still about what happened in 1980 in country Y. So we still can't answer
the question. Statement number two. In 1980, the median household
income in country Y was 1/2 the median household income
in country X in 1980. Now, you might be tempted to
say, oh, two linear equations and two unknowns, maybe I can
solve for it, et cetera. But no. There's actually two
linear equations in four unknowns, right? 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, Y80 over Y70, we'll know what the percent
decline was. Right? If this number is 0.8, then
it would be a 20% decline. If this number was 0.5, then
it would be a 50% decline. So whatever this number is,
that's essentially 1 minus that is the percent decline. So maybe we just have
to figure out this. But look. I can prove to you
mathematically that we still can't figure it out
without this. Because Y80 divided by Y70,
that's equal to 2/3X-- oh no, sorry, Y80. So Y80, that's 1/2X in 1980
divided by 2/3X in 1970. Right? And then let's see. If we could take this 3/2
up, we get, let's see-- divide by 1/3. 3 becomes 3/2. So it becomes 3/4X80 over X70. They never told us what the
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? So the total amount--
let's see. Donation is going to be equal
to x dollars times the number of 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's 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 we getting
for each car. So that is not enough
information by itself. Statement two. 60 more cars were sold
than expected. So the total amount actually
donated was $28,000. Interesting. 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. 60 more cars 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? 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. If I just said 560x is equal to
$28,000, then you get 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 number
of cars that were expected to be sold. Times 500. And actually, yeah, you have to
have statement one there, because statement two-- 60
more cars were sold. Actually, let me think
about that. So both combined, when I use
both of the information, it definitely works. So let me see if I can figure
it out just using statement two alone. I don't think I can, but I have
a nagging feeling that they may be giving more
information than I'm-- so let me say that the cars
expected is C. So this is what statement two
actually is telling us. I assumed the 500, which
I shouldn't have done. So statement two is actually
telling, when I have 60 more than the cars expected
to be sold times x, I raised $28,000. Right. This alone is not-- you don't
know what x or C is. Because at the end of the
day you need to know what x times C is. x times C is our goal. So if you distributed this out,
you get xC plus 60x is equal to $28,000. And you get xC is equal
to 28,000 minus 60x. So this is as much information
as you can glean just from statement number two. So that alone is not enough. 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 would just know. Well actually, that's true
with 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 sometimes I might
even get them wrong. Problem 93. While driving on the expressway,
did Robin ever exceed the 55 mile an
hour speed limit? Well, who knows? Statement one. Robin 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 100 miles. Two. Robin drove for 2 hours
on the expressway. So time is equal to 2 hours. So each of these independently
give me no information about how fast she went. But if I use both of
them, I can figure out her average speed. I can say, well, she went
100 miles in 2 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 miles an hour. Well, we don't know how fast
her car accelerates. She might just gone-- she
accelerated really fast, got to 55, stayed there or went down
a little bit and ended up averaging at 55. She's 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 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'd know that she had to exceed
the speed limit. Because, well, we can assume
that at some some point 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. OK. This sounds like
a Venn Diagram. French or Spanish or both. So this is French,
this is Spanish. And this right here is both,
in the intersection. If 100 of these students do not
study French-- OK, they study French or Spanish
or both. There's not an option
to do neither. If 100 of these students do not
study French, how many of these students study both
French and 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 garish color. Oh, no. That's not what I want to do. That tells us that this area
right here is 100. So essentially, the people who
are studying Spanish but not French is 100. 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. Not this, just this. So that tells us how many
study French only. That's 60. It still doesn't help us to
know the intersection. Statement number two says, a
total of 240 of the students 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 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 100. 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 two gives us enough
information, by itself, to solve the problem. And we don't even need
statement number one. and I'm out of time. See you in the next video.