### 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.