- [Sal] We're told that Joe started
his math homework.
He finished 23 problems by himself.
He finished 13 more problems with help from Sal.
I don't know if they're talking about me or not.
And then they say there are nine math problems left.
And then they ask us,
how many math problems did Joe have when he started?
So, pause this video and see if you can work through that
before we do it together.
All right, so the way my brain thinks about it
is there's some amount that he started with.
So, let's put a big bar over here.
This is some amount that Joe started with.
So, let me write that, starting amount.
And then he was able to do many of them,
so he's finished 23 problems by himself.
So, let me draw 23 here.
So, he was able to finish 23 by himself.
Then he finished 13 more with help
from someone with my name, maybe it's me.
So, then he did 13 more with help from Sal.
So, that's 13 right over there.
And then the total amount left was nine.
So, the total amount left has to be able to finish up,
be just as long as our starting amount.
So, this is nine right over here.
So, this is left, thus, 23 was the ones he did by himself.
The 13 was with help from me and then he had nine left.
So, if you wanna know the starting amount,
how many math problems did Joe have when he started,
you have to add together 23 plus 13 plus nine.
So, how do we do that?
Well, let's do it one at a time.
So, let's just think about how many he finished,
and then we can add to that how many is left,
and that's the starting amount.
So, the amount that he finished.
So, that's this amount right over here,
the ones he did by himself, plus the ones he did with Sal.
That's going to be 23 plus 13.
Now, 23 plus 13 is the same thing,
if I just think about it, I have two tens here,
so that's 20 plus three,
plus 10 plus three.
That one is in the tens place.
Plus 10 plus three.
Well, that's the same thing as if I just look at the,
if I just look at the tens right over there.
20 plus 10,
plus three plus three.
20 plus 10 is 30.
So, this is going to be equal to 30,
plus three plus three is six.
So, this is going to be equal to 36.
So, this whole amount right over here,
the amount of problems that Joe either did by himself,
or with the help of Sal, that is 36 problems.
And so, to figure out the starting amount,
we just have to figure out the total that he did,
plus how many are left to get the starting amount.
So, what is 36 plus nine?
Well, the way my brain thinks about it,
let me just do it right over here.
36 plus nine is equal to what?
Well, this is the same thing as 30 plus six plus nine,
and six plus nine, you may already know is 15.
Another way you could think about it
is if you start at nine, you have to add one to get to 10,
and then you have five left over from the six to get to 15.
So, another way to rewrite this,
30 plus 15 is the same thing
as 30 plus 10 plus five.
30 plus 10, this right over here, that's 40.
So, it's going to be 40 plus five which is equal to 45.
So, Joe had 45 problems when he started.
He did 23 by himself, then he did 13,
and he would have nine left.
And you would see if you start with 45,
and if you were to subtract 23 and then subtract 13,
you actually would indeed have nine left.