Solving Proportions With 2 Variables

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When solving proportions with two variables, the problem can be simplified once it's understood what variable is being solved. Solve proportions with multiple variables through cross multiplication with help from a math teacher in this free video on proportions in math.

Part of the Video Series: Fractions & Proportions
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One variable is bad enough. How do you solve a proportion problem with two variables? Hi. I'm Jimmy Chang, I've been teaching college mathematics for nine years. And when you have two variables as opposed to one, it does make the problem seem a little tougher but once you know what variable you want to solve for, you just treat it like any other algebra problem as long as you're consistent with your strategies. So here's a basic example as to how to do this. Suppose you have one proportion, three over x equals to four over y. Now let's just suppose the directions are solve for y. So that means that you have to get y by itself. But the thing is because you have two proportions, you still solve it the exact same way, like you would normal proportion problems and that is via cross multiplication. So for example, take the x, multiply it with the four. So you will have 4x. And then take the y and then multiply it with the three and you will have 3y. Now since your objective is to solve for y, you want to isolate the y term. Now because the y has been multiplied with the three, you want to get rid of that. So you want to divide both sides by three. So as a result, the threes will cancel and you'll have y is equal to four thirds x. And then since you solve for y, you are finished. Now if the directions say solve for x instead. And you have the same problem, you still do the cross multiplication, so your terms will still be the same. So you have 3y is equal to 4x, but this time you want to solve for x. You want to isolate the x term. So being that four is being multiplied with the x, you would divide both sides by 4. An so as a result the fours will cancel and you are left with 3y over 4 and that is what x will end up being. So whatever variable you want to solve for, as long as you follow the rules of cross multiplication, you can solve proportion problems with two variables. I'm Jimmy and that's a glimpse as to how to solve proportion problems using two variables.

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