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比例問題另一種解法 (新高畫質英語)

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比例問題另一種解法 (新高畫質英語) : 用另外一種解法

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It's always good to see the same problem done more than one
way, and it's especially true with these ratio problems
because they, in general, can be done in many, many different
ways, and different types of ways gel with different people.
So I just did a video on this where I said that the
ratio of apples to oranges starts off at five to eight.
And we take away fifteen.
We take away fifteen apples, and the ratio becomes one to four.
And then the question that we have to answer is how much
total fruit do we have after taking away the fifteen apples?
And we figured it out.
We figured out that it's fifty pieces of fruit.
But let's see if we can do it a different way.
The last time I kind of talked through it and
used a lot of words.
Let see if we can do it a little bit more algebraically.
So let a is equal to the number of apples we are starting with,
and let o equal the number of oranges.
That doesn't change throughout the whole problem.
So we're starting off with a apples and o oranges.
So the ratio of a to o is equal to what?
The ratio of a-- let me actually-- well, instead of
trying to fit this whole problem into this part of the
screen, let me just copy and paste this part, and do it at
the bottom part of the screen.
Let me copy it, and then let me scroll down here where I have
some extra real estate because I think I'm going to need more
than that little pocket of area right there.
So I copied and pasted just like that.
OK, so there we have it.
a is the number of apples to start with, and o is
the number of oranges.
So we could write-- let me do it in a color that
I haven't used before.
I actually haven't used white.
So we can say that the ratio of apples to oranges
is equal to five to eight.
That's what they tell us, that the number of apples we start
with divided by the number of oranges, or the ratio of them--
i have to be a little bit more particular-- is five to eight.
Then we removed fifteen apples.
So if we remove fifteen apples, how many apples do we have?
We have a minus fifteen apples.
And they tell us that the ratio-- then the ratio of
apples to oranges becomes one to four.
So a minus fifteen, which is the number of apples we start with
minus fifteen, the ratio of that to oranges is equal to one over four.
And let's see if we can solve these two equations.
I have two equations here, and I have two unknowns.
Let's see what we can do here.
And I should probably shouldn't have labeled-- there's a reason
why o isn't used in algebra a lot, because it looks just
like a zero, but I'll try to be careful.
So this first-- let me write down my two
equations over here.
It never hurts to rewrite it.
The original apples to oranges ratio is five to eight.
Then when we remove fifteen apples, the ratio of our new number of
apples to oranges is equal to one over four.
This is just an algebraic way of stating our problem.
Let's see if we can solve this.
If we cross-multiply both sides of this equation,
we get eighta is equal to fiveo.
That's not a zero.
It's equal to fiveo.
Or if we subtract fiveo from both sides, get eighta
minus fiveo is equal to zero.
So this is just a linear equation with two unknowns.
Now, what do we get on this right-hand side?
If we cross-multiply, we get foura minus sixty.
I'm just multiplying four times a minus fifteen.
That is equal to one times o, or we could just write--
well, I'll write oneo.
That's not a ten.
That's oneo, or one orange.
And if we rearrange this, if we subtract the oneo from both
sides, we get foura minus oneo minus sixty is equal to zero.
Or if we add sixty to both sides, we get foura minus
oneo is equal to sixty.
And here, you might recognize that these are just two
linear equations right here.
That's one of them, and that's the second of them.
And I have two unknowns.
I have a and o.
I probably should have called them x and y to prevent this o
from looking so confusing because that's a zero
and that's an o.
But I think you get what I'm saying.
So how do we solve this?
Well, what we can do is we can multiply one of these times a
convenient factor, and then add them or subtract them to
get rid of one of the two variables, so let's do that.
Let's multiply this equation times minus two, so it becomes
minus eighta plus twoo is equal to minus one hundred and twenty.
I just multiplied this equation right here times minus two.
If I do that and then if I add it to this equation right here,
this equation is eighta minus fiveo is equal to zero, what do I get?
Let's just add these two equations.
This becomes zeroa.
Minus five plus two is minus threeo is equal to minus one hundred and twenty, or o is
equal to-- you divide both sides-- you can ignore this.
You divide both sides by minus three, you get o is equal to forty.
So let's see.
So the oranges is equal to forty.
And that's before and after.
The o never changes.
o is equal to forty.
So what are our apples equal to?
We could go to either of these equations.
We could go to any of these that we have.
Maybe we can go to this one.
So we have eight times our number of apples is equal to five times
the number of oranges, or five times forty.
eight times the number of apples is equal to two hundred, or the apples is
equal to two hundred over eight, which is equal to one hundred over four,
which is equal to twenty-five.
So remember what a and o are.
O is the number of oranges we have throughout the problem.
a is the number of apples we start with.
That's what we start with.
So you can say that we start with twenty-five apples, forty oranges,
or we start with sixty-five pieces of fruit.
Then if you remove fifteen fruit, you'll end up with fifty fruit,
which is the exact same answer we got the other way of doing
this problem, and it's nice to see it done two ways.
If you want to know the number of apples we end up with,
we started with twenty-five apples.
If you were to take fifteen away from them, you're going
to get ten apples.
So you start with twenty-five apples, forty oranges, sixty-five fruit.
You end with ten apples, forty oranges, or fifty fruit.
Either way.
Hopefully, it was reasonably useful to see this
done another way.

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比例問題另一種解法 (新高畫質 英語)

比例問題另一種解法 (新高畫質 英語) : 用另外一種解法

比例問題另一種解法 (新高畫質英語)

比例問題另一種解法 (新高畫質英語) : 用另外一種解法