### Video Transcript

Rachel organised a barn dance, washed some cars, and took part in a sponsored run to raise money for a charity. She recorded the money that she raised in a table. Write down the ratio for the amount of money raised washing cars to the total amount raised. Give the ratio in its simplest form.

We need two values: we need to work out the amount of money she raised simply washing cars and the total amount she raised altogether. She washed 15 cars and she charged 10 pounds per car. This means that the total amount raised washing cars can be found by multiplying 15 by 10. When we multiply by 10, we move the digits to the left one space. So 15 multiplied by 10 is 150 and she raised 150 pounds washing cars.

We can then work out the total amount she raised by adding 224, then that 150, and the amount for the sponsored run which is 212. Now, if necessary, we could use a column method to do so. But this is a calculator paper. So we can type this in and that gives us a value of 586 pounds.

All that’s left is to put this in a ratio. Remember order matters. So the amount of money raised washing cars goes first and the total amount goes second. That gives us a ratio of 150 to 586.

Remember though we wanted a ratio in its simplest form. So we need to reduce these numbers somewhat. We can see that they’re both even. So let’s start by dividing both of the numbers by two.

150 divided by two is 75 and 586 divided by two is 293. We cannot reduce these numbers any further. 75 and 293 are coprime; that is to say, the only factor they have in common now is one.

We can do a quick check. We can see that neither of the numbers are even. So they can’t be divided by two. We can type into our calculator 75 divided by three and 293 divided by three and see that when we divide 293 by three, we get a noninteger, a nonwhole number.

We can repeat this process for all of the prime numbers that we can think of: five, seven, eleven, and so on. And that tells us that in its simplest form the ratio of the amount of money raised washing cars to the total amount raised is 75 to 293.