I was interrupted in the last video by a phone call.
I was actually expecting a phone call from someone whose
call I wanted to take, but that ended up being one of
those robocallers.
So, anyway, I was on problem 163.
Let me just start it over so that I don't interrupt your
train of thought.
A fruit salad mixture consists of apples, peaches, and grapes
in the ratio of 6:5:2.
So the ratio of apples to peaches to grapes is equal to
6:5:2 by weight.
If 39 pounds of the mixture is prepared, the mixture include
how many more pounds of apples than grapes?
So they essentially want us to figure out what the apples
minus the grapes are equal to.
So we have 39 pounds, so the pounds of apples plus the
peaches plus the grapes, that equals 39 pounds.
And to do a ratio problem like this, the easiest way is to
say let's just define the number of pounds of apples
being 6 times some number x.
If the apples are 6 times some number x,
what are the peaches?
We know that the ratio of the apples to the peaches are 6:5,
so the peaches are going to have to be 5
times some number x.
By the same logic, the grapes are going to have to be 2
times some number x.
And if you try out the ratio the apples to the grapes is 6x
over 2x, which is 6:2.
So it all works out.
So let's use this information to substitute back there and
see what x is equal to.
So we get 6x plus 5x plus 2x is equal to 39.
6 plus 5 is 11 plus 2 is 13.
13x is equal to 39.
x is equal to 3.
And so how many apples are there?
6x, there are 18 apples.
We don't have to figure out the peaches, but we can do it
fast. There are 15 peaches, and then there are 6 grapes.
And if you want to know how many more apples there are
than grapes, 18 minus 6 is equal to 12-- actually these
are all in pounds.
There are 12 pounds more of apples than grapes.
And that's choice B.
Problem 164.
Louise has x more dollars than Jim has.
So L is equal to Jim plus x, and together they have a total
of y dollars.
So L plus J is equal to y.
Which of the following represents the number of
dollars that Jim has?
So they want Jim equals, and they want it in
terms of x and y.
So let's take this L and substitute it here so that we
have an equation that this has J's, x's, and y's in it.
So if L is equal to J plus x, we can substitute.
So we get J plus x, instead of an L, plus J is equal to y.
That is that, just that.
And you get 2J plus x is equal to y.
Subtract x from both sides.
2J is equal to y minus x.
And we get J is equal to y minus x over 2.
And that is choice A.
Problem 165.
Let's switch colors.
During a certain season, a team won 80% of its first 100
games, and 50% of the remaining.
If the team won 70% of its games for the entire season,
so they won 70% of the total, what was the total number of
games that the team played?
So how do we figure out the total number of games that
they played?
It'll be 100 plus remainder.
So let's think of it this way.
If we wanted to figure out the total percentage that they
won, we would want the number that they won.
So how many games did they win?
They won 80% of their first 100 games, so that's 80 games,
plus 50% of the remainder games.
So plus 0.5 times the remainder.
That's how many games they've won.
Now, how many games did they play?
The total number of games is going to be 100 plus whatever
this remainder number of games are.
That's their total number of games.
And the problem tells us that this ratio, the total
percentage-- this is of all the games they won divided by
all the games they played-- that that is
equal to 0.7 or 70%.
If we multiply both sides of this equation by 100 plus r,
we get 80 plus 0.5r is equal to-- 0.7 times 100 is equal to
70 plus 0.7r.
Now let's subtract 70 from both sides.
You get 10 plus 0.5r is equal to 0.7r.
And then if we subtract 0.5r from both sides, we get 10 is
equal to 0.2r, or r is equal to 10 over 0.2.
And 10 over 0.2, 0.2 is the same thing as 1/5.
So this is 10 times 5, so that's equal to 50.
So the remainder games were 50, so they want to know the
total number of games the team plays.
So it's going to be the first 100 games plus
the remainder games.
So 100 plus 50.
They played 150 games, which is choice D.
We're on problem 166.
Of 30 applicants for a job, 14 had at least 4 years of
experience.
So experience greater than 4, we have 14.
I just make up notation as we go.
Of 30 applicants for a job, 14 had at least 4 years of
experience, 18 had degrees-- so we say degrees, we have
18-- and 3 had less than 4 years of experience and did
not have a degree.
So experience was less than 4 years' experience and no
degree, and that is 3 people.
How many of the applicants had at least 4 years of experience
and a degree?
So let's see how we can think about it.
There's 30 applicants for a job.
So let me draw our universe.
If I did all of the applicants, let me
draw it like this.
So that's the whole applicant universe, and that's 30.
And we know that 14 had more than 4 years of experience.
Let me do that in this color.
So this attribute, I'll make it look like that, so that's
the 14 that have experience greater than 4 years.
And that's 14 of them.
And then 18 have a degree.
And I'm assuming that there's some overlap between the
degrees in the 14.
We don't know that for sure, but let's say that this point
right here I'll draw another circle.
So let's say that circle looks something like that.
So let's call this the degreed people.
And there's 18 of them in this whole circle.
And then they say that there were 3 people with experience
less than 4 and no degree.
So they're outside of both of these circles.
So this right here is 3.
Now, what are they asking?
I've already forgotten that.
How many of the applicants had at least 4 years experience
and a degree?
So they're asking for this intersection right here.
So there's one question we can answer.
What's the sum of this population, the population
that has more than 4 years of experience or a degree?
So let me circle.
What's this sum right here?
This and this.
It's going to be whatever's left after you take out the 3
people who have nothing.
So that's going to be 27 people.
So 27 people have at least 4 years of
experience or a degree.
Now, how can relate that to the 14 and 18?
So what happens if we just add the 14 and the 18?
When we have the 14, we're going to count
these people once.
And if we were add that to 18, we would count
these people twice.
So if we wanted this number-- if we wanted the number of
people who are in this circle or this circle-- what we would
want to do is add the 14 to the 18, but then subtract out
once the people who are this intersection.
Let's call them B.
That's a B.
I know you can't read it.
Let's say there B people in that intersection.
You'll subtract that out once.
I want that to really make sense for you.
If we want to know the total number of people in this
circle and this circle combined, when we say 18
people, that's including some people here.
And if we were add that to 14 people, where once again some
of those 14 are here again, are these people.
So when we just add 18 to 14, we're counting this twice.
So if we want to know the actual number in the circle or
the circle, since we add 18 to 14 we count it twice, we wants
to subtract these people out once.
Hopefully that makes sense.
But anyway, now we're ready to solve.
We get 27 is equal to-- 14 plus 18 is
equal to 32 minus B.
27 from both sides, you get 0 is equal 5 minus B.
Add B the both sides.
You get B is equal to 5.
And that is choice E.
See you in the next video.