We are trying to get our unknown number, x, on the left side of the equation, all by itself.
Since x is multiplied by 20, we can use the "inverse" of multiplying, which is dividing, to get rid of the 20.
A proportion is simply a statement that two ratios are equal.
It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d.
Well, we're using three times more oatmeal, Right? 3 cups of oatmeal and 9 cups of oatmeal, we're using 3 times the oatmeal.
Well, if we want to use flour in the same proportion, we have to use 3 times the flour.
If you're behind a web filter, please make sure that the domains *.and *.are unblocked. And there's a bunch of different ways to solve this. Or another way to write 10/8, 10/8 is the same thing as 5/4. You could do that without thinking in strict algebraic terms. If I multiply these out, this guy and that guy cancel out, and it's definitely 360. But now we want to actually divide this to actually get our right answer, or a simplified answer. So let's rewrite our proportion, 8/36 is equal to 10/n. Well the easiest way to solve for n is maybe multiply both-- this thing on the left is equal to this thing on the right. These guys cancel out and we're left with n is equal to 10 times 36 is 360/8.
And I'll explore really all of them, or a good selection of them. So we're multiplying by 5/4 to get to 10, from 8 to 10. And so we could say this n, this thing that we just solved for, this n is going to be equal to 36 times 5 divided by 4. 8 goes into 360, 8 goes into 36 4 times, 4 times 8 is 32. And notice, we're getting the exact same value that we got with cross-multiplying.
So if you multiply the numerator by 9/2, you get the denominator. So then we'll get 10 times 9/2 is going to be equal to n, is going to be equal to this denominator. And so you're saying 8 times what is equal to 360. If any of the ways before this worked, that's fine.
Then to figure out what the denominator here is, if we want the same fraction, we have to multiply by 9/2 again. Now the last thing I'm going to show you involves a little bit of algebra.