# Solving Percent Equations 03:08 minutes

**Video Transcript**

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Transcript
**Solving Percent Equations**

Richard the mage has fallen head over heals for the beautiful princess, Ms. Morgaine. He's madly in love, but she doesn't like him one bit. He wants to make his great-grandmother's love potion number 9 to make the princess fall in love with him forever.

To brew potion number 9, he needs to calculate a few **percent equations**, as percents are part of the recipe. To make 200 ml of the potion, which is one full dose, he'll need to mix these ingredients:

- 20% honey
- ½ of a bat wing
- 50 teardrops of love
- 17.5% unicorn horn extract

### Percent Equation Example 1

Some of these are listed as **percentages of the full** 200 ml potion. In particular, the honey and unicorn horn extract. How can he figure out how much of each ingredient he must use?

So if honey makes up 20% of the whole potion, we must find 20% of 200ml. We can use the **formula, part over whole equals percent over 100**, to start answering this question.

For the amount of honey, which is unknown, we use x. Now let's **substitute**: 20 percent of the love potion is honey, so we'll substitute percent with 20. And since 200ml is the full amount of the potion, we substitute 200 for the whole. To find the part, which is our unknown, we can call it x.

We can use **cross multiplication** to get rid of the **denominators**. That gives us the **equation** 100 · x = 20 · 200. We can simplify this to 100x = 4000.

Finally, we can solve for x by dividing both sides by 100. We see that x = 40. So 20% of the full 200ml potion is equal to 40ml of honey. Great, Richard can make the potion now. But wait – one more ingredient is still written in percent: Unicorn horn extract.

### Percent Equation Example 2

17.5 percent of 200ml is what we are looking for. Let's use our formula again and subsitute: 17.5% for the percent, 200 for the whole, and x for the unknown part.

Once again we **cross-multiply** and get 100 · x = 17.5 times 200. We can simplify to 100x = 3500. Now we use **opposite operations** and **divide both sides** by 100. Doing so, we find that x = 35.

Therefore, Richard must use 35 ml of unicorn horn extract. Now he can finally make the potion to make the princess fall hopelessly in love with him... when suddenly (pooof)... And, well, Richard can't explain this very well but the racoon has started to look extremely beautiful to him.

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