Yousef, Ezra, and Joshua split some money between themselves in the ratio of four to three to three. Yousef’s share was 108 pounds. What was the original amount of money that they split between themselves?
A common mistake here is to think that we need to share 108 pounds between the three children. In fact, we’re told that Yousef’s share alone was 108 pounds. Let’s look back at the original ratio.
Since order does matter, Yousef has four parts, Ezra has three parts, and Joshua also has three parts of the original amount of money. Since Yousef’s share was 108 pounds, we can see that these four parts are worth 108 pounds. We should use this information to find the value of one part.
Since four parts are worth 108 pounds, we can divide 108 by four to get the value of one part. We can use the bus-stop method here. We can’t do one divided by four using this method. So instead, we work out how many fours make 10. That’s two with a remainder of two. 28 divided by four is seven. This means that 108 divided by four is 27. And one part must be worth 27 pounds.
Now, at this point, we could work out what Ezra and Joshua got, individually. Since one part is worth 27 pounds, we can multiply this by three to work out the value of Ezra’s share and Joshua’s share. However, we’re trying to find the original amount of money that they split. We can see that they split it up into a total of 10 parts, since four plus three plus three is equal to 10.
We said that one part is worth 27 pounds. So to work out the value of 10 parts and the total amount of money that they shared, we can multiply 27 by 10. To multiply by 10, we move all the digits to the left one place. 27 multiplied by 10 then is 270. And 270 pounds was the original amount of money that they split between themselves.