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# Ratio problem with basic algebra

A slightly more involved ratio problem with algebra. Created by Sal Khan.

Video transcript

Now that have a basic
understanding of what a ratio is, let's see if we can tackle
some more advanced problems. So, I have a classroom. It's got 55 students in it. 55 students. And I also know that the ratio
of boys to girls, the ratio of I'll write it this way,
boys to girls is 4:7. What I want to know is, how
many girls do I need to add. So, how many girls need to add,
or do I need to add, do I need to add, for the ratio, for
the ratio to become 1:2. 1:2. And this is the ratio
of boys to girls. I'm not switching
the ratio on you. So, right now for every
4 boys, I have 7 girls. I want to add some girls so
that the ratio becomes for every boy, I have 2 girls. So how can you do this? Well, just going back to the
basic ratio video, the first thing we can do we, know the
total number of students. And we know the ratio. So maybe it'll help us to
figure out the number of boys and girls we have right now. So our current ratio is 4:7. So boys, boys, to girls,
right now is equal to 4:7. That means -- what
does that mean? That means for every, if
you add up these two. For every 11 students there
are 4 boys and 7 girls. There are 4 boys, 4
boys and 7 girls. That's what this
ratio tells us. You give me 11 students of
this -- you could split this classroom into
a bunch of groups. And for every group of 11,
you're going to have 4 boys and 7 girls that's
all that tells me. For every 11 students,
4 boys and 7 girls. If you split them, every
group has the same number of boys and girls. Now, how many groups of
11 students there are? So there are 55 students. We have 55 students total. And we're breaking them
into groups of 11. And every group will
have the same number of boys and of girls. So we have 11 groups. Sorry, if we divide by
11 students per group. Students per group. So how many groups of 11
students do we have? That means we have 5
groups of 11 students. 5 groups of 11 students. And we've done this
drill before. Every group has 4 boys
and it has 7 girls. So we have 5 groups. 5 groups each of them has 4
boys, that means we have 5 times 4, which is
equal to 20 boys. And we have 5 times 7, we
have 5 groups, 5 times 7, each group has 7 girls. Of girls. So that's equal to 35 girls. And the numbers add up. 20 plus 35 is 55. And 20 to 35, 20 to
35, is equal to 4:7. So it all works out. So that's what we
have right now. Now, we're going to add to
girls to the classroom to change the ratio. So let's do this. So right now we have 20 boys. We have 20 boys. And we have 35 girls. We just figure that out. And I'm going to add some
girls to the classroom. So I'm going to add some girls
to the classroom And my new ratio, after I add these g
girls to the classroom, my new ratio is going to be 1:2. 1:2. So I have an equation
I have one unknown, I can just solve for it. You can almost do this
one in your head. 20 is to what, 1 is to
2 as 20 as to what? You could say, oh, 20 is -- 1
is 1/2 of 20, 20 is 1/2 of 40. So you could say, oh, it's 40. So g would be equal to 5. That's how you would
solve it in your head. If you want to do it
algebraically, you could cross-multiply. So you get 35 plus g times 1. So you get 35 plus g is
equal to 2 times 20. Is equal to 40, which
is essentially what we did in our head. We said, hey, this thing
has to be equal to forty. So, if you subtract 35
from both sides, you get g is equal to 5. So if you add 5 girls to your
classroom, you're going to have 40 girls. So then you'd have 40 girls. And you have 20 boys. And your ratio is 20:40,
which is 2:4, which is the same thing is 1:2. And we've done our problem.