### Video Transcript

If 10π₯ is equal to 11π¦ which is
equal to 12π§, find the ratio of π₯ to π¦ to π§.

There are lots of ways of solving
this problem. One way would be to find values
that solve different parts of the equation first. Letβs begin by considering 10π₯ is
equal to 11π¦. Substituting in the values π₯
equals 11 and π¦ equals 10 would mean that this equation is true. 10 multiplied by 11 and 11
multiplied by 10 are both equal to 110. This means that the ratio of π₯ to
π¦ could be written as 11 to 10. Letβs now consider the fact that
10π₯ is also equal to 12π§. In this equation, π₯ equals 12 and
π§ equals 10 is a solution. 10 multiplied by 12 and 12
multiplied by 10 are both equal to 120. This means that the ratio of π₯ to
π§ is 12 to 10.

We now have two ratios, a ratio of
π₯ to π¦ and a ratio of π₯ to π§. In order to combine these ratios,
we need to use equivalent ratios to ensure that the value for π₯ is the same. The lowest common multiple of 11
and 12 is 132. We can therefore multiply the top
ratio by 12 and the bottom ratio by 11. The ratio 11 to 10 is equivalent to
the ratio 132 to 120. Likewise, the ratio of π₯ to π§ of
12 to 10 is equivalent to 132 to 110. As our value for π₯ is the same, we
can now combine the ratios. The ratio of π₯ to π¦ to π§ is 132
: 120 : 110.

This ratio can be simplified as all
of our values are even and are therefore divisible by two. 132 divided by two is equal to
66. 120 divided by two is equal to
60. And 110 divided by two is equal to
55. The ratio of π₯ to π¦ to π§ in its
simplest form is 66 : 60 : 55 as these three numbers have no common factor apart
from one.