Solving Proportions Using Cross Products
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.
|Number and Quantity||Reason quantitatively and use units to solve problems|
|Ratios, Percentages, and Proportions||Proportions|
If there are 36 Coins, what is the total number of items in the pot?
We want to find the total number of items, so let’s call our variable i.
Now let’s set up our ratios as Coins to Total Items. We can also write that as a fraction.
The number of Coins is 36. So Coins over Total Items is the same as 36 over i.
Now let’s set up an equivalent ratio for Coins to Total Items.
We have 2 coins to every 3 shamrocks, giving us 5 total items, so we know that 2 out of
every 5 items are coins.
So the equivalent ratio would be 2 over 5. Because we have found the equivalent ratio,
we can set up a formula: Thirty-six over i equals two-fifths. Now we solve for i.
Using the method of cross products, we know that 36 times 5 will equal 2 times i.
36 times 5 equals 180. So 180 equals 2i. Next, divide both sides by 2 to get i equals 90..
The total number of items in Leonard’s pot is 90.
Leonard, it looks like you’ll be getting some green so you can go out and buy… well…