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Complex Proportions

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In this video, we will be learning how to solve complex proportions (variables on both sides) using cross-multiplication.

For Example:

\frac{x}{20}=\frac{(x+1)}{30}\leftarrow First we cross-multiply

30x=20(x+1)\leftarrow Then we distribute the 20 to the x and 1

30x-20x=20x +20-20x\leftarrow Subtract 20x from both sides to isolate x

\frac{10x}{10}=\frac{20}{10}\leftarrow Divide by 10 on both sides

x=2

Complex Proportions

Video-Lesson Transcript

Let’s go over complex proportions.

For example:

\dfrac{x}{20} = \dfrac{x + 1}{30}

What makes this complex is that we have one variable on both sides of the equation.

We’re just going to do the same method which is to cross-multiply.

x \times30 = 30x

To solve the equation on the right, we have to distribute 20 on each of term.

{x + 1} \times20 20x + 20

Now we have

30x = 20x + 20

Let’s get all the variables on one side by subtracting 20x on both sides.

30x - 20x = 20x - 20x + 20 10x = 20

Simply solve x by dividing both sides by 10.

\dfrac{10x}{10} = \dfrac{20}{10}

And we’ll have

x = 2

Complex proportion is different from regular proportion because it has a variable on both sides of the equation.