# Video: Pack 3 • Paper 1 • Question 11

Pack 3 • Paper 1 • Question 11

04:05

### Video Transcript

There are some plain, some chocolate, and some raisin biscuits in a jar. There are exactly 16 chocolate biscuits in the jar. The ratio of the number of plain biscuits to the number of chocolate biscuits to the number of raisin biscuits is two to eight to five. Calculate the number of plain biscuits in the jar.

In the question, we’re given that the ratio of plain to chocolate to raisin biscuits is two to eight to five. And what this means is that for every eight chocolate biscuits, there has to be two plain biscuits and five raisin biscuits.

Now, the other piece of information given to us in the question is that there are exactly 16 chocolate biscuits in the jar. And so therefore, we could rewrite our ratio as something to 16 to something, where this first question mark represents the number of plain biscuits in the jar and the second question mark represents the number of raisin biscuits in the jar.

In this part of the question, however, we’re only interested in finding the number of plain biscuits. So let’s focus on that. Now, we can compare the two ratios which we have. We see that to go from the first ratio to the second ratio, the number in the middle — so that’s the number that represents the number of chocolate biscuits — has doubled or multiplied by two. So therefore, in order to go from the first ratio to the second ratio, the other parts of the ratio must also double.

Therefore, we find that the number of plain biscuits in the jar will be two multiplied by two, giving us four biscuits. We’ve now answered the first part of the question since we found the number of plain biscuits in the jar to be four. Let’s move on to part b.

Lisa adds some more raisins biscuits to the jar. Given that the ratio of the number of plain biscuits to the number of chocolate biscuits to the number of raisin biscuits is now one to four to five, find the number of raisin biscuits that Lisa adds to the jar.

Let’s start by finding how many raisin biscuits were originally in the jar. Similarly to part a, we simply multiply the ratio by two to find the number of biscuits. So multiplying the five by two, we see that there were originally 10 raisin biscuits in the jar. Next, we need to find the number of raisin biscuits that are in the jar after Lisa added some more.

We know that the ratio of plain to chocolate to raisin biscuits is now one to four to five since this was given to us in the question. We also know that the number of plain biscuits and the number of chocolate biscuits in the jar from part a has not changed. So we still have four plain biscuits and 16 chocolate biscuits.

So we know that the current ratio of biscuits in the jar is four to 16 to something, where something is the number of raisin biscuits which are currently in the jar. Since this ratio must be equivalent to one to four to five, we just need to find what number we multiply one to four to five by in order to get this ratio of four to 16 to something.

Clearly, we can see that we multiply the one by four to get four and we multiply the four by four to get 16. So therefore, we must also multiply the five by four in order to find the number of raisin biscuits, which are currently in the jar. So five timesed by four gives us 20 raisin biscuits.

Now, we note that the question asked us to find the number of biscuits which Lisa added to the jar. So this will simply be the difference between the number of biscuits which are in the jar after she added them and the number of biscuits which were in the jar before she added them. And so this gives us 20 minus 10, telling us that Lisa has added 10 raisin biscuits to the jar. And this is our answer.