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Solving Proportions using Cross Products, a la Shmoop.

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Leonard the Leprechaun has run into some financial troubles and needs to sell his pot o’ gold

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on eBay. The pot contains Shamrocks and Golden Coins.

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The ratio of Shamrocks to Coins is 3 to 2.

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Meaning that, for every 3 shamrocks he has in his pot, he has 2 coins.

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If there are 36 Coins, what is the total number of items in the pot?

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We want to find the total number of items, so let’s call our variable i.

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Now let’s set up our ratios as Coins to Total Items. We can also write that as a fraction.

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The number of Coins is 36. So Coins over Total Items is the same as 36 over i.

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Now let’s set up an equivalent ratio for Coins to Total Items.

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We have 2 coins to every 3 shamrocks, giving us 5 total items, so we know that 2 out of

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every 5 items are coins.

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So the equivalent ratio would be 2 over 5. Because we have found the equivalent ratio,

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we can set up a formula: Thirty-six over i equals two-fifths. Now we solve for i.

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Using the method of cross products, we know that 36 times 5 will equal 2 times i.

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36 times 5 equals 180. So 180 equals 2i. Next, divide both sides by 2 to get i equals 90..

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The total number of items in Leonard’s pot is 90.

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Leonard, it looks like you’ll be getting some green so you can go out and buy… well…

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more green.

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