ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Solving Proportions Using Cross Products 6802 Views


Share It!


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.

Up Next

SAT Math 10.3 Geometry and Measurement
3336 Views

SAT Math 10.3 Geometry and Measurement. What is the ratio of birds to dogs?

Related Videos

SAT Math 2.1 Statistics and Probability
343 Views

SAT Math 2.1 Statistics and Probability. Which two items have the highest protein to fat ratio?

SAT Math 2.2 Statistics and Probability
242 Views

SAT Math 2.2 Statistics and Probability. What percent of her recommended daily intake of 2000 calories did she consume?

SAT Math 4.2 Statistics and Probability
233 Views

SAT Math 4.2 Statistics and Probability

SAT Math 4.4 Geometry and Measurement
210 Views

SAT Math 4.4 Geometry and Measurement