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Solving Proportions Using Cross Products 6802 Views


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Description:

This video covers how to use cross products to solve for a missing number in a proportion by setting that proportion with a variable over the product equal to its equivalent ratio.

Language:
English Language

Transcript

00:04

Solving Proportions using Cross Products, a la Shmoop.

00:08

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

00:12

on eBay. The pot contains Shamrocks and Golden Coins.

00:19

The ratio of Shamrocks to Coins is 3 to 2.

00:22

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

00:28

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

00:32

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

00:39

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

00:45

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

00:53

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

00:57

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

01:04

every 5 items are coins.

01:06

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

01:09

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

01:16

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

01:21

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

01:35

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

01:39

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

01:56

more green.

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