# Video: Pack 4 β’ Paper 3 β’ Question 16

Pack 4 β’ Paper 3 β’ Question 16

02:22

### Video Transcript

π΄, π΅, πΆ, and π· are four points on a straight line in that order. π΄π΅ to π΅π· is five to three. π΄πΆ to πΆπ· is three to one. Find the ratio π΄π΅ to π΅πΆ to πΆπ·.

Now, the first thing Iβve done is just drawn a representation of actually what this could look like, so our line π΄, π΅, πΆ, and π·. Itβs not to scale. But it gives us an idea of where they might be. First of all, if we think about our ratio π΄π΅ to π΅π·, then this is five to three. So Iβve marked on our diagram, so the five for π΄π΅ and then π΅ to π· is three. And then, we also have our ratio π΄πΆ to πΆπ· and this is three to one. And again, Iβve actually marked this onto our diagram.

Well, the first thing we know and we can actually summarize from our diagram is that π΄π΅ is going to be five-eighths of the total length and Iβve marked that on there. This is gonna be useful and Iβll show you why now. Well, also, in addition, we know that πΆπ· is a quarter of the total length. So now, weβve actually got two parts and we know the fraction of the total of length that they are.

So therefore, using that, what we can actually do is actually work out the fraction that π΅πΆ is going to be because π΅πΆ is gonna have to be one minus five over eight minus one-quarter. So therefore, we can actually calculate that because itβs gonna be one minus five-eighths minus two-eighths and thatβs because a quarter is the same as two-eighths. And what Iβve done is multiplied the numerator and denominator by two. So therefore, we can say that π΅πΆ is gonna be one-eighth of the total length. And thatβs because weβve got π΅πΆ, at one-eighth, plus π΄π΅, at five-eighths, makes six-eighths plus πΆπ·, at a quarter, which is two-eighths makes eight-eighths or one whole. So that is the total length.

So now, we take a look back at the question and we see whatβs it actually looking for. What itβs looking for is the ratio π΄π΅ to π΅πΆ to πΆπ·. Well, if we think about it again, if we got it in this order, weβve got π΄π΅ is five-eighths to π΅πΆ which is one-eighth to πΆπ· which is two-eighths.

Therefore, we get the final answer which is our ratio π΄π΅ to π΅πΆ to πΆπ· which is five to one to two. And weβve actually got this ratio because we had five-eighths to one-eighth to two-eighths and they all have the same denominator. So we can simplify that to five to one to two.